Zhibin Du and Bo Zhou: Maximum Degree Distance of Graphs with Exactly Two Cycles, p.119-136

Abstract:

The degree distance of a connected graph $G$ with vertex set $V(G)$ is defined as $D'(G)=\sum\limits_{u\in V(G)}d_G(u)D_G(u)$, where $d_G(u)$ is the degree of vertex $u$ and $D_G(u)$ is the sum of distances between $u$ and all vertices of $G$. We determine the maximum degree distances in the class of connected graphs with exactly two vertex-disjoint cycles and in the class of connected graphs with exactly two cycles of a common vertex, respectively, and then the maximum degree distance in the class of connected graphs with exactly two cycles. The extremal graphs are characterized.

Key Words: Degree, distance, Wiener index, cycle, graph.

2000 Mathematics Subject Classification: Primary: 05C07;
Secondary: 05C90, 92E10.

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