Discrete Mathematics & Theoretical Computer Science, Vol 17, No 3 (2016)

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The irregularity of two types of trees

Li Jianxi, Yang Liu, Wai Chee Shiu


The irregularity of a graph G is defined as the sum of weights |d(u)-d(v)| of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, some structural properties on trees with maximum (or minimum) irregularity among trees with given degree sequence and trees with given branching number are explored, respectively. Moreover, the corresponding trees with maximum (or minimum) irregularity are also found, respectively.

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