Cacti with the maximum Merrifield–Simmons index and given number of cut edges

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• 作者：Maolin Wang
• 关键词：Cactus ; Merrifield– ; Simmons index ; Cut edge ; Extremal graph
• 刊名：Applied Mathematics Letters
• 出版年：2010
• 出版时间：December 2010
• 年：2010
• 卷：23
• 期：12
• 页码：1416-1420
• 全文大小：285 K

文摘

The Merrifield–Simmons index of a graph G, denoted by i(G), is defined to be the total number of its independent sets, including the empty set. A graph G is called a cactus if each block of G is either an edge or a cycle. Denote by the set of connected cacti possessing n vertices and k cut edges. In this work, we shall characterize the cacti with the maximum Merrifield–Simmons index among all graphs in for all possible values of k.