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arXiv · 1711.04095

The energy change of the complete multipartite graph

Hai-Ying Shan·Chang-Xiang He·Zhen-Sheng Yu
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Abstract

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Akbari et al. \cite{S. Akbari} proved that for a complete multipartite graph $K_{t_1 ,\ldots,t_k}$, if $t_i\geq 2 \ (i=1,\ldots,k)$, then deleting any edge will increase the energy. A natural question is how the energy changes when $\min\{t_1 ,\ldots,t_k\}=1$. In this paper, we will answer this question and completely determine how the energy of a complete multipartite graph changes when one edge is removed.

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Hai-Ying Shan, Chang-Xiang He, Zhen-Sheng Yu. 2017-11-11. The energy change of the complete multipartite graph. https://arxiv.org/abs/1711.04095

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