Paper Info
Title
The least Q-eigenvalue with fixed domination number.
Abstract
Denote by Lg, l the lollipop graph obtained by attaching a pendant path P=vgvg+1⋯vg+l (l ≥ 1) to a cycle C=v1v2⋯vgv1 (g ≥ 3). A Fg,l−graph of order n≥g+1 is defined to be the graph obtained by attaching n−g−l pendent vertices to some of the nonpendant vertices of Lg, l in which each vertex other than vg+l−1 is attached at most one pendant vertex. A Fg,l∘-graph is a Fg,l−graph in which vg is attached with pendant vertex. Denote by qmin the least Q−eigenvalue of a graph. In this paper, we proceed on considering the domination number, the least Q-eigenvalue of a graph as well as their relation. Further results obtained are as follows: (i)some results about the changing of the domination number under the structural perturbation of a graph are represented;(ii)among all nonbipartite unicyclic graphs of order n, with both domination number γ and girth g (g≤n−1), the minimum qmin attains at a Fg,l-graph for some l;(iii)among the nonbipartite graphs of order n and with given domination number which contain a Fg,l∘-graph as a subgraph, some lower bounds for qmin are represented;(iv)among the nonbipartite graphs of order n and with given domination number n2.
Year
DOI
Venue
2018
10.1016/j.amc.2018.07.055
Applied Mathematics and Computation
Keywords
Field
DocType
Domination number,Signless Laplacian,Nonbipartite graph,Least eigenvalue
Graph,Combinatorics,Vertex (geometry),Mathematical analysis,Domination analysis,Eigenvalues and eigenvectors,Mathematics
Journal
Volume
ISSN
Citations 
339
0096-3003
0
PageRank 
References 
Authors
0.34
5
4
Name
Order
Citations
PageRank
Guanglong Yu12811.07
Mingqing Zhai2186.26
Chao Yan379.62
Shu-Guang Guo412.42