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The least Q-eigenvalue with fixed domination number

Author

Listed:
  • Yu, Guanglong
  • Zhai, Mingqing
  • Yan, Chao
  • Guo, Shu-guang

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.

Suggested Citation

  • Yu, Guanglong & Zhai, Mingqing & Yan, Chao & Guo, Shu-guang, 2018. "The least Q-eigenvalue with fixed domination number," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 477-487.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:477-487
    DOI: 10.1016/j.amc.2018.07.055
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    References listed on IDEAS

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    1. Liping Zhang & Haibo Jiang & Shuguang Guo, 2014. "Cluster Anticonsensus of Multiagent Systems Based on the -Theory," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-7, April.
    2. Liping Zhang & Haibo Jiang, 2012. "Impulsive Cluster Anticonsensus of Discrete Multiagent Linear Dynamic Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-11, March.
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