On degree distance of some composite graphs

Authors

  • Hongbo Hua

Keywords:

Degree distance, double graph, extended double cover, edge copied graph

Abstract

Let $G$ be a connected simple graph. The degree distance of $G$ is defined as $D^{'}(G)=\sum\limits_{u\in V(G)}d_{G}(u)D_{G}(u)$, where $D_{G}(u)$ is the sum of distances between the vertex $u$ and all other vertices in $G$ and $d_{G}(u)$ denotes the degree of vertex $u$ in $G$. In contrast to many established results on extremal properties of degree distance, few results in the existing literatures deal with degree distance of composite graphs. Towards filling in this gap, we study the degree distance of some composite graphs here. We present explicit formulae for $D^{'}(G)$ of three composite graphs, namely, double graphs, extended double covers and edge copied graphs. DOI: 10.1017/S0004972711002711

Published

2011-12-09

Issue

Vol. 85 No. 1 (2012)

Section

Articles
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