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The irregularity of two types of trees

Abstract : 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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Li Jianxi, Yang Liu, Wai Shiu. The irregularity of two types of trees. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2016, Vol. 17 no. 3 (3), pp.203-216. ⟨hal-01352840⟩

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