Extremal (balanced) blow-ups of trees with respect to the signless Laplacian index

Huiqing Liu, Mei Lu and Jing Zhao

Applied Mathematics and Computation, 2023, vol. 453, issue C

Abstract: For a positive integer vector a=(a1,a2,…,ak) and a graph T with V(T)={v1,v2,…,vk}, the a-blow-up of T, denoted by T(a), is the graph that arises from T by replacing every vertex vi of T with an ai-clique Kai (1≤i≤k), where Kaj is adjacent to Kas in T(a) if and only if vj is adjacent to vs in T. When all ai (1≤i≤k) are equal to some positive integer a, the corresponding blow-up is called balanced. In this paper, the extremal graphs with the maximum signless Laplacian index among all a-blow-ups of trees with k vertices are first characterized, and then the minimum signless Laplacian index among all balanced blow-ups of trees with k vertices is determined.

Keywords: Blow-up; Tree; Signless Laplacian index (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:453:y:2023:i:c:s0096300323002679

DOI: 10.1016/j.amc.2023.128098

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