Consider a graph G with vertex set V(G) and edge set E(G). A subset D of V(G) is said to be a dominating set of G if every vertex not in D is adjacent to at least one vertex in D. If, in addition, every vertex not in ...
详细信息
Consider a graph G with vertex set V(G) and edge set E(G). A subset D of V(G) is said to be a dominating set of G if every vertex not in D is adjacent to at least one vertex in D. If, in addition, every vertex not in a dominating set R of G is adjacent to at least one vertex in V(G)-R, then R is called a restrained dominating set of G. A paired restraint dominating set S of a graph G is a restrained dominating set of G satisfying that the induced subgraph by S contains a perfect matching. The problems of computing the dominating set, restrained dominating set, and paired restraint dominating set with minimum cardinality are referred to as the domination, restrained domination, and paired restraint domination problems, respectively. The paired restraint domination problem and its applications are first proposed here. Our focus is on examining the complexity of the proposed problem on extended supergrid graphs and their subclasses, which include grid, diagonal supergrid, and (original) supergrid graphs. The domination problem is known to be NP-complete on grid graphs and, therefore, also on extended supergrid graphs. Our previous research demonstrated that the domination and restrained domination problems on diagonal and original supergrid graphs are NP-complete. However, the complexity of the paired restraint domination problem on grid, diagonal supergrid, and original supergrid graphs remains unknown. The NP-completeness of the paired restraint domination problem on diagonal supergrid graphs is demonstrated in this paper, and this finding is also applicable to the original supergrid graphs and planar graphs with maximum degree 4. We then examine a subclass of diagonal and original supergrid graphs known as rectangular supergrid graphs. These graphs are distinguished by a rectangular shape consisting of m rows and n columns of vertices. Specifically, we address the paired restraint domination problem on Rm×n and develop a linear time algorithm for 3⩾m⩾1 and n⩾m. Then
Disasters, both natural and man-made, pose significant risks to human life and infrastructure, necessitating swift and efficient search and rescue (SAR) operations. Traditional SAR methods often struggle to access haz...
详细信息
Von Willebrand disease (VWD) is a blood disorder caused by a protein deficiency that prevents blood from clotting properly. The challenge faced by people with Von Willebrand disease is having access to limited informa...
详细信息
作者:
Manikandan, R.Kumar, K. SatheshRamkumar, S.
Department of Lean Operations and Systems Karnataka Bengaluru India Alliance University
Computer Science and Engineering Alliance College of Engineering and Design Karnataka Bengaluru India
Department of Computer Science Karnataka Bengaluru India
Most of the Active Noise Cancellation (ANC) systems working properly in low-frequency noises only. To make it suitable for isolating high-frequency noise, it needs an additional circuit which consumes more energy. Thi...
详细信息
The spreading of false information over the internet, highly impacts society and causes social and economic loss to the nation. One of the most important factors for the increase in the number of misleading informatio...
详细信息
作者:
Pisal, TejasKumar, HemantKumar, PraveenGote, Pradanyawant
Faculty of Engineering & Technology Department of Computer Science & Design Wardha Maharashtra Sawangi442001 India
Faculty of Engineering & Technology Department of Basic Sciences and Humanities Wardha Maharashtra Sawangi442001 India
Faculty of Engineering & Technology Department of Computer Science & Medical Engineering Wardha Maharashtra Sawangi442001 India
Acute sinusitis, often occurring as a consequence of recovering from a cold, presents a significant health concern due to its impact on the interconnected hollow spaces located behind the cheekbones, forehead, and nos...
详细信息
The importance of renewable energy in our everyday lives cannot be overstated, specifically highlighting solar and wind energies as two crucial sustainable power sources. Nevertheless, it is crucial to acknowledge tha...
详细信息
Autonomous driving involves complex decision-making in highly interactive environments, requiring thoughtful negotiation with other traffic participants. While reinforcement learning provides a way to learn such inter...
详细信息
This study presents a pilot study on the potential future use of aerial sound sources utilizing parametric array loudspeakers (PALs) in drones via fifth-generation (5G) networks. Integrating superdirectional loudspeak...
详细信息
In chart-based programming environments for machine knitting, patterns are specified at a low level by placing operations on a grid. This highly manual workflow makes it challenging to iterate on design elements such ...
详细信息
暂无评论