Graphs with given number of cut vertices and extremal MerrifieldSimmons index

Hongbo Hua; Shenggui Zhang

doi:10.1016/j.dam.2011.03.008

Graphs with given number of cut vertices and extremal MerrifieldSimmons index

Hongbo Hua, Shenggui Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The MerrifieldSimmons index of a graph is defined as the total number of its independent sets, including the empty set. Denote by G(n,k) the set of connected graphs with n vertices and k cut vertices. In this paper, we characterize the graphs with the maximum and minimum MerrifieldSimmons index, respectively, among all graphs in G(n,k) for all possible k values.

Original language	English
Pages (from-to)	971-980
Number of pages	10
Journal	Discrete Applied Mathematics
Volume	159
Issue number	10
DOIs	https://doi.org/10.1016/j.dam.2011.03.008
State	Published - 28 Jun 2011

Keywords

Bound
Cut vertex
Extremal graph
Independent sets
MerrifieldSimmons index

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10.1016/j.dam.2011.03.008

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abstract = "The MerrifieldSimmons index of a graph is defined as the total number of its independent sets, including the empty set. Denote by G(n,k) the set of connected graphs with n vertices and k cut vertices. In this paper, we characterize the graphs with the maximum and minimum MerrifieldSimmons index, respectively, among all graphs in G(n,k) for all possible k values.",

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AB - The MerrifieldSimmons index of a graph is defined as the total number of its independent sets, including the empty set. Denote by G(n,k) the set of connected graphs with n vertices and k cut vertices. In this paper, we characterize the graphs with the maximum and minimum MerrifieldSimmons index, respectively, among all graphs in G(n,k) for all possible k values.

KW - Bound

KW - Cut vertex

KW - Extremal graph

KW - Independent sets

KW - MerrifieldSimmons index

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ER -

Graphs with given number of cut vertices and extremal MerrifieldSimmons index

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Keywords

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