2013/10/17 by Guanglong Yu, Shu-Guang Guo, Yu, Guanglong +6
Computer Science · Materials Science · Mathematics · #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Synthesis and properties of polymers #math.CO #msc:05C50
paper · pdf · doi:10.48550/arxiv.1310.4717
13 pages, 3 figures
arxiv created 2013/10/17 · openalex publication_date 2013/10/17 · arxiv updated 2013/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A vertex set D of a graph G is said to be a dominating set if every vertex of V(G)∖ D is adjacent to at least a vertex in D, and the domination number γ(G) (γ, for short) is the minimum cardinality of all dominating sets of G. For a graph, the least Q-eigenvalue is the least eigenvalue of its signless Laplacian matrix. In this paper, for a nonbipartite graph with both order n and domination number γ, we show that n≥ 3γ-1, and show that it contains a unicyclic spanning subgraph with the same domination number γ. By investigating the relation between the domination number and the least Q-eigenvalue of a graph, we minimize the least Q-eigenvalue among all the nonbipartite graphs with given domination number.