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arXiv · 2306.16747

Spectral extremal graphs for edge blow-up of star forests

Jing Wang·Zhenyu Ni·Liying Kang·Yi-zheng Fan
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Abstract

The edge blow-up of a graph $G$, denoted by $G^{p+1}$, is obtained by replacing each edge of $G$ with a clique of order $p+1$, where the new vertices of the cliques are all distinct. Yuan [J. Comb. Theory, Ser. B, 152 (2022) 379-398] determined the range of the Tur\'{a}n numbers for edge blow-up of all bipartite graphs and the exact Tur\'{a}n numbers for edge blow-up of all non-bipartite graphs. In this paper we prove that the graphs with the maximum spectral radius in an $n$-vertex graph without any copy of edge blow-up of star forests are the extremal graphs for edge blow-up of star forests when $n$ is sufficiently large.

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Jing Wang, Zhenyu Ni, Liying Kang, Yi-zheng Fan. 2023-06-29. Spectral extremal graphs for edge blow-up of star forests. https://arxiv.org/abs/2306.16747

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