scholarly journals The number of independent sets of unicyclic graphs with given matching number

2012 ◽  
Vol 160 (1-2) ◽  
pp. 108-115 ◽  
Author(s):  
Gong Chen ◽  
Zhongxun Zhu
Keyword(s):  
Independent Sets ◽  
Matching Number ◽  
Unicyclic Graphs

scholarly journals On the nullity and the matching number of unicyclic graphs

2009 ◽  
Vol 431 (8) ◽  
pp. 1293-1301 ◽  
Author(s):  
Ji-Ming Guo ◽  
Weigen Yan ◽  
Yeong-Nan Yeh
Keyword(s):  
Matching Number ◽  
Unicyclic Graphs

scholarly journals The number of independent sets in unicyclic graphs

2005 ◽  
Vol 152 (1-3) ◽  
pp. 246-256 ◽  
Author(s):  
Anders Sune Pedersen ◽  
Preben Dahl Vestergaard
Keyword(s):  
Independent Sets ◽  
Unicyclic Graphs

scholarly journals The harmonic index of unicyclic graphs with given matching number

2014 ◽  
Vol 38 (1) ◽  
pp. 173-183 ◽  
Author(s):  
L.V. Jian-Bo ◽  
Jianxi Li ◽  
Shiu Chee
Keyword(s):  
Matching Number ◽  
Unicyclic Graphs ◽  
Harmonic Index

scholarly journals Unicyclic graphs with given number of cut vertices and the maximal Merrifield-Simmons index

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 451-461 ◽  
Author(s):  
Hongbo Hua ◽  
Xinli Xu ◽  
Hongzhuan Wang
Keyword(s):  
Connected Graph ◽  
Independent Sets ◽  
Unicyclic Graph ◽  
Unicyclic Graphs

The Merrifield-Simmons index of a graph G, denoted by i(G), is defined to be the total number of independent sets in G, including the empty set. A connected graph is called a unicyclic graph, if it possesses equal number of vertices and edges. In this paper, we characterize the maximal unicyclic graph w.r.t. i(G) within all unicyclic graphs with given order and number of cut vertices. As a consequence, we determine the connected graph with at least one cycle, given number of cut vertices and the maximal Merrifield-Simmons index.

scholarly journals On symmetric division deg index of unicyclic graphs and bicyclic graphs with given matching number

2021 ◽  
Vol 6 (8) ◽  
pp. 9020-9035
Author(s):  
Xiaoling Sun ◽  
◽  
Yubin Gao ◽  
Jianwei Du
Keyword(s):  
Matching Number ◽  
Unicyclic Graphs ◽  
Symmetric Division ◽  
Bicyclic Graphs
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