Two subgraph grafting theorems on the energy of bipartite graphs

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• 作者：Changxiang He^a ; ^{changxiang-he@163.com} ; Lin Lei^a ; Haiying Shan^b ; Anni Peng^b
• 关键词：05C50 ; 15A18
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：515
• 期：Complete
• 页码：96-110
• 全文大小：385 K
• 卷排序：515

文摘

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. The subgraph grafting operation on a graph is a kind of subgraph moving between two vertices of the graph. In this paper, we introduce two new subgraph grafting operations on bipartite graph and show how the graph energy changes under these subgraph grafting operations. As the application of these operations, we determine the trees with the third and fourth minimal energies in the set of trees with given order and domination number.