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L(0,1)-labelling of Permutation Graphs

Journal of Mathematical Modelling and Algorithms in Operations Research 2015年第4期14卷 469-479页

作者： Paul, Satyabrata Pal, Madhumangal Pal, Anita Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 India Department of Mathematics National Institute of Technology Durgapur Durgapur 713209 India

L(0,1)-labelling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The goal of L(0,1)-labelling problem is to produce a legal labelling that minimize the largest label used. In this article, it is shown that, for a permutation graph G with maximum vertex degree Δ, the upper bound of λ_0,1(G) is Δ−1. Finally, we prove that the result is exact for bipartite permutation graph. © 2015, Springer Science+Business Media Dordrecht.

关键词： Frequency assignment problem L(0,1)-labelling Permutation graph

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An inventory model under development cost-dependent imperfect production and reliability-dependent demand

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Journal of Management Analytics 2017年第3期4卷 258-275页

作者： Barun Khara Jayanta Kumar Dey Shyamal Kumar Mondal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar UniversityMidnaporeWBIndia Department of Mathematics Mahishadal Raj CollgePurba MedinipurWBIndia

This paper considers a model that deals with an imperfect production process where both perfect and imperfect quality items are ***,demand depends on selling price and reliability of the *** manufacturing company expects to produce perfect quality *** due to the long-run process,several kinds of problem such as labor,machinery,and technology *** a result,the manufacturing system becomes out-of-control state and consequently produces both perfect and imperfect quality *** items are ready to sell but imperfect items are reworked at a cost to become *** cost,reliability of the product and reliability parameter of the manufacturing system can be improved by introducing the development cost and also by improving the quality of the raw material of the production *** such circumstances,a profit function has been developed to find the optimum values of reliability parameter of the manufacturing system,reliability of the product and duration of production such that a manufacturer gets a maximum ***,the model has been illustrated with some numerical examples exploring the sensitivity analysis with respect to some parameters.

关键词： imperfect production production time reliability parameter reliability of product

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Analysis of Road Map Design Based on Multigraph with Picture Fuzzy Information

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International Journal of applied and Computational mathematics 2020年第3期6卷 1-17页

作者： Das, Sankar Ghorai, Ganesh Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India Department of Mathematics Kharagpur College Kharagpur 721 305 India

In this paper, the picture fuzzy planar graph is defined along with some basic properties of picture fuzzy graph. The notion of picture fuzzy planar graphs is introduced and the terms such as strong (weak) edges, strong (weak) picture fuzzy planar graphs, strength of an edge, degree of planarity, picture fuzzy faces, strong (weak) picture fuzzy faces, picture fuzzy dual graphs and picture fuzzy combinatorial dual graphs are defined. Some theorems on degree of planarity and picture fuzzy combinatorial dual graphs have been established. An application of picture fuzzy planar graph in the design of road maps is given. © 2020, Springer Nature India Private Limited.

关键词： Picture fuzzy combinatorial dual graph Picture fuzzy dual graphs Picture fuzzy graphs Picture fuzzy planar graphs Strong (weak) picture fuzzy planar graphs

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Two-stage multi-item 4-dimensional transportation problem with fuzzy risk and substitution

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Journal of Ambient Intelligence and Humanized Computing 2023年第7期14卷 9469-9496页

作者： Devnath, Sudeshna De, Manoranjan Mondal, Seema Sarkar Maiti, Manoranjan Department of Mathematics National Institute of Technology Durgapur Durgapur713209 India Department of Mathematics Mugberia Gangadhar Mahavidyalaya West Bengal Purba Medinipur India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore721102 India

With the worldwide transport infrastructural development, there are several connecting roads between the cities for transportation. Some of these roads are smooth, and some are very rough, which invites some risks during transportation. For public distribution of some commodities, Govts. of developing countries collect those from the open markets, transport those to some warehouses for temporary storage, and from there, again transport to the fair-price shops for public distribution. With these facts, in this investigation, Govt.’s above scheme is modelled as two-stage four-dimensional transportation problems with different choices of conveyances and routes. There are some path and conveyance-wise uncertain travel risks. In fair-price shops, substitutable essential items (say rice and wheat) are sold with the necessary ones (say, mustard oil, etc.), which are sold by push-sale against some concession in an essential item (say, more rice, etc.). Thus, there is a trade-off between the ‘push-sale’ and ‘concession’, and hence an optimum decision is derived. Several models are developed depending on management’s and customers’ decisions, substitutability, push-sale, and environments. For road risk, a two-parameter (road’s roughness and distance) Mamdani-type fuzzy logic is implemented. The system’s profits for different models are maximised in both crisp and fuzzy environments and illustrated numerically using Generalised Reduced Gradient method through Lingo software. Here, the Govt.’s policy of introducing new products (termed as necessary item) among the public against a concession in an essential item has been introduced and analysed. This push-sale is effective up to a certain level, and after that, profit goes down. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

关键词： Fuzzy logic

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Fuzzy k-competition graphs

Fuzzy k-competition graphs

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2013 Science and Information Conference, SAI 2013

作者： Pal, Madhumangal Samanta, Sovan Pal, Anita Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore-721102 India Department of Mathematics National Institute of Technology Durgapur 713209 India

ISBN: (纸本)9780989319300

Fuzzy competition graph as the generalization of competition graph is introduced here. A generalization of fuzzy competition graph known as fuzzy k-competition graph is also defined. These graphs are related to fuzzy digraphs. Fuzzy neighbourhood graphs, which are related to fuzzy graphs are defined here. Some relations between fuzzy competition graphs and fuzzy neighbourhood graphs have been established. Also several results to find strong edges of the stated graphs are obtained. © 2013 The Science and Information Organization.

关键词： Graphic methods

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Inverse Fuzzy Mixed Planar Graphs with Application

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International Journal of applied and Computational mathematics 2024年第4期10卷 1-13页

作者： Mondal, Rahul Ghorai, Ganesh Department of Mathematics Vivekananda Satavarshiki Mahavidyalaya Manikpara West Bengal Jhargram 721513 India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

The idea of inverse fuzzy mixed graph (IFMG) was firstly introduced by Poulik and Ghorai (Granul Comput 7:549–559, 2021) in 2021 generalizing the idea of fuzzy mixed graphs. Here the idea of planarity is introduced in the more generalized setting of IFMGs using the concept of intersecting value. The concept of effective edges and strong planar graphs are given. Also the idea of I-considerable edges and I-considerable numbers have been discussed at the end. Several properties of IFMGs are studied. Finally an application is discussed using these concepts. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

关键词： Intersecting value Inverse fuzzy (multi) graphs Inverse fuzzy mixed graphs Planarity value

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Interval Oriented Entropy Based Multi-item Solid Transportation Problem with Budget and Breakability

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International Journal of applied and Computational mathematics 2015年第2期1卷 279-292页

作者： Baidya, Abhijit Bera, Uttam Kumar Maiti, Manoranjan Department of Mathematics National Institute of Technology Agartala Jirania 799055 West Tripura India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721102 WB India

To maximization the total profit and minimization the total cost we investigate two transportation models with interval transportation parameters and we present a solution of our newly developed models using appropriate methods. The solid transportation problem has been formulated with and without interval entropy function defined by Shannon’s measure of entropy. Also an additional constraint on the total budget at each destination is imposed. When we transport the goods from plants to destination then few items should be damage due to bad condition of route and vehicles, for this reason we introduce the breakability in our respective models. We employ two different approaches (Hu and Wang’s Approach and Mahato and Bhunia’s Approach) based on interval ranking and made a comparison on it. To convert the multi-objective programming problem into single-objective problem we apply weighted sum method. The models are illustrated with numerical examples and solved using the LINGO.13 optimization software. The results of the models with and without entropy are also obtained and compared. © 2014, Springer India Pvt. Ltd.

关键词： Breakability Budget constraint Entropy function Interval order relation Solid transportation problem (STP) Weighted sum method

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Application of Bipolar Fuzzy Sets in Planar Graphs

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International Journal of applied and Computational mathematics 2017年第2期3卷 773-785页

作者： Akram, Muhammad Samanta, Sovan Pal, Madhumangal Department of Mathematics University of the Punjab New Campus Lahore Pakistan Department of Mathematics JKHS Tamluk India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore 721 102 India

A bipolar fuzzy set is a generalization of a fuzzy set. In this paper, we apply the concept of bipolar fuzzy sets to multigraphs and planar graphs. We introduce the notions of bipolar fuzzy multigraphs, bipolar fuzzy planar graphs, bipolar fuzzy dual graphs, and investigate some of their interesting properties. We also study isomorphism between bipolar fuzzy planar graphs. © 2016, Springer India Pvt. Ltd.

关键词： Bipolar fuzzy dual graphs Bipolar fuzzy graphs Bipolar fuzzy multigraphs Bipolar fuzzy planar graphs

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Colouring of COVID-19 Affected Region Based on Fuzzy Directed Graphs

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computers, Materials & Continua 2021年第7期68卷 1219-1233页

作者： Rupkumar Mahapatra Sovan Samanta Madhumangal Pal Jeong-Gon Lee Shah Khalid Khan Usman Naseem Robin Singh Bhadoria Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar UniversityMidnapore721102India Department of Mathematics Tamralipta MahavidyalayaTamluk721636India Division of Applied Mathematics Wonkwang UniversityIksan-SiJeonbuk54538Korea School of Engineering RMIT UniversityMelbourne3001Australia School of Computer Science University of Sydney Sydney2006Australia Department of Computer Science&Engineering Birla Institute of Applied Sciences(BIAS)BhimtalUttarakhand263136India

Graph colouring is the system of assigning a colour to each vertex of a *** is done in such a way that adjacent vertices do not have equal *** is fundamental in graph *** is often used to solve real-world problems like traffic light signalling,map colouring,scheduling,***,social networks are prevalent systems in our ***,the users are considered as vertices,and their connections/interactions are taken as *** users follow other popular users’profiles in these networks,and some don’t,but those non-followers are connected directly to the popular *** means,along with traditional relationship(information flowing),there is another relation among *** depends on the domination of the relationship between the *** type of situation can be modelled as a directed fuzzy *** the colouring of fuzzy graph theory,edge membership plays a vital *** membership is a representation of flowing information between end nodes of the *** from the communication relationship,there may be some other factors like domination in *** influence of power is captured *** this article,the colouring of directed fuzzy graphs is defined based on the influence of *** with this,the chromatic number and strong chromatic number are provided,and related properties are *** application regarding COVID-19 infection is presented using the colouring of directed fuzzy graphs.

关键词： Graph colouring chromatic index directed fuzzy graphs

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Dynamics of cholera outbreak with bacteriophage and periodic rate of contact

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International Journal of Dynamics and Control 2016年第3期4卷 284-292页

作者： Panja, Prabir Mondal, Shyamal Kumar Chattopadhyay, Joydev Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University MidnaporeW.B.721 102 India Agricultural and Ecological Research Unit ISI 203 B.T.Road Kolkata India

In this paper, a cholera epidemic model with periodic transmission rate has been considered and discussed. It is shown that the disease free equilibrium point is globally asymptotically stable and also seen that the cholera disease is disappeared if the basic reproduction number is less than one. When the basic reproduction number is grater than one, then the endemic equilibrium is globally asymptotically stable. Finally, numerical simulations have been given for the existence of the analytical results. © 2015, Springer-Verlag Berlin Heidelberg.

关键词： Bacteriophages

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