Degree resistance distance of unicyclic graphs

Document Type: Research Paper

Authors

1 University of Kragujevac Kragujevac, Serbia

2 Department of Mathematics, Central South University

Abstract

Let $G$ be a connected graph with vertex set $V(G)$‎. ‎The‎ ‎degree resistance distance of $G$ is defined as $D_R(G) = \sum_{\{u‎, ‎v\} \subseteq V(G)} [d(u)+d(v)] R(u,v)$‎, ‎where $d(u)$ is the degree‎ ‎of vertex $u$‎, ‎and $R(u,v)$ denotes the resistance distance between‎ ‎$u$ and $v$‎. ‎In this paper‎, ‎we characterize $n$-vertex unicyclic‎ ‎graphs having minimum and second minimum degree resistance‎ ‎distance‎.

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