The least Q-eigenvalue with fixed domination number

Guanglong Yu, Mingqing Zhai, Chao Yan and Shu-guang Guo

Applied Mathematics and Computation, 2018, vol. 339, issue C, 477-487

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 leastQ−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.

Keywords: Domination number; Signless Laplacian; Nonbipartite graph; Least eigenvalue (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:477-487

DOI: 10.1016/j.amc.2018.07.055

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