2012
DOI: 10.7151/dmgt.1646
|View full text |Cite
|
Sign up to set email alerts
|

Sharp bounds for the number of matchings in generalized-theta-graphs

Abstract: A generalized-theta-graph is a graph consisting of a pair of end vertices joined by k (k ≥ 3) internally disjoint paths. We denote the family of all the n-vertex generalized-theta-graphs with k paths between end vertices by Θ n k . In this paper, we determine the sharp lower bound and the sharp upper bound for the total number of matchings of generalized-theta-graphs in Θ n k . In addition, we characterize the graphs in this class of graphs with respect to the mentioned bounds.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1

Citation Types

0
1
0

Year Published

2012
2012
2012
2012

Publication Types

Select...
1

Relationship

1
0

Authors

Journals

citations
Cited by 1 publication
(1 citation statement)
references
References 9 publications
(6 reference statements)
0
1
0
Order By: Relevance
“…Recently, many researchers have offered various results about extremal problems in computing the total number of matchings (z-index) or the total number of independent sets (Merrifield-Simmons index) for some classes of graphs. For example trees [8,9,15,21], trees with fixed number of leaves [19,24], trees with fixed diameters [16], trees with fixed maximum degrees [21], quasi-trees [12], unicyclic graphs [11,14,18,20,23], bicyclic graphs [1,2,3,4], generalized-theta-graphs [6], and tricyclic graphs [5,7,13] are some special classes of graphs that have been worked on. For more information, [22] is a nice survey paper on the topics.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, many researchers have offered various results about extremal problems in computing the total number of matchings (z-index) or the total number of independent sets (Merrifield-Simmons index) for some classes of graphs. For example trees [8,9,15,21], trees with fixed number of leaves [19,24], trees with fixed diameters [16], trees with fixed maximum degrees [21], quasi-trees [12], unicyclic graphs [11,14,18,20,23], bicyclic graphs [1,2,3,4], generalized-theta-graphs [6], and tricyclic graphs [5,7,13] are some special classes of graphs that have been worked on. For more information, [22] is a nice survey paper on the topics.…”
Section: Introductionmentioning
confidence: 99%