Extremal Values of the Atom-Bond Connectivity Index for Trees with Given Roman Domination Numbers

作     者：Ali, Waqar Husin, Mohamad Nazri Bin Nadeem, Muhammad Faisal 

作者机构：Special Interest Group on Modeling and Data Analytics Faculty of Computer Science and Mathematics Universiti Malaysia Terengganu Terengganu Kuala Nerus21030 Malaysia Department of Mathematics COMSATS University Islamabad Lahore Campus Lahore54000 Pakistan 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Trees (mathematics) 

摘      要：Consider that G = (X, Y) is a simple, connected graph with X as the vertex set and Y as the edge set. The atom-bond connectivity (ABC) index is a novel topological index that Estrada introduced in Estrada et al. (1998). It is defined as ABC(G) = xy∈XY (G)s ζx +ζxζζyy− 2 where ζx and ζx represent the degrees of the vertices x and y, respectively. In this work, we explore the behavior of the ABC index for tree graphs. We establish both lower and upper bounds for the ABC index, expressed in terms of the graph’s order and its Roman domination number. Additionally, we characterize the tree structures that correspond to these extremal values, offering a deeper understanding of how the Roman domination number (RDN) influences the ABC index in tree graphs. © 2024, CC BY.