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

Author

Listed:
  • LIU, Huiqing
  • LU, Mei
  • ZHAO, Jing

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.

Suggested Citation

  • LIU, Huiqing & LU, Mei & ZHAO, Jing, 2023. "Extremal (balanced) blow-ups of trees with respect to the signless Laplacian index," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    • Handle: RePEc:eee:apmaco:v:453:y:2023:i:c:s0096300323002679
    DOI: 10.1016/j.amc.2023.128098
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