### Bicyclic graphs with maximum degree resistance distance

#### Abstract

Graph invariants, based on the distances between the

vertices of a graph, are widely used in theoretical chemistry.

Recently, Gutman, Feng and Yu ({\it Transactions on Combinatorics},

01 (2012) 27-40) introduced the {\it degree resistance distance} of

a graph $G$, which is defined as $D_{R}(G)=\sum_{\{u,v\}\subseteq

V(G)}[d_G(u)+d_G(v)]R_G(u,v)$, where $d_G(u)$ is the degree of

vertex $u$ of the graph $G$, and $R_G(u,v)$ denotes the resistance

distance between the vertices $u$ and $v$ of the graph $G$. Further,

they characterized $n$-vertex unicyclic graphs having minimum and

second minimum degree resistance distance. In this paper, we

characterize $n$-vertex bicyclic graphs

having maximum degree resistance distance.

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