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- W4284962597 abstract "Let $G$ be a graph of size $m$ and $rho(G)$ be the spectral radius of its adjacency matrix. A graph is said to be $F$-free if it does not contain a subgraph isomorphic to $F$. In this paper, we prove that if $G$ is a $K_{2,r+1}$-free non-star graph with $mgeq (4r+2)^2+1$, then $rho(G)leq rho(S_m^1)$, with equality if and only if $Gcong S_m^1$. Recently, Li, Sun and Wei showed that for any $theta_{1,2,3}$-free graph of size $mgeq 8$, $rho(G)leq frac{1+sqrt{4m-3}}{2}$, with equality if and only if $Gcong S_{frac{m+3}{2},2}$. However, this bound is not attainable when $m$ is even. We proved that if $G$ is $theta_{1,2,3}$-free and $Gncong S_{frac{m+3}{2},2}$ with $mgeq 22$, then $rho(G)leq rho(F_{m,1})$ if $m$ is even, with equality if and only if $Gcong F_{m,1}$, and $rho(G)leq rho(F_{m,2})$ if $m$ is odd, with equality if and only if $Gcong F_{m,2}$." @default.
- W4284962597 created "2022-07-10" @default.
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- W4284962597 creator A5066056488 @default.
- W4284962597 date "2022-07-06" @default.
- W4284962597 modified "2023-09-24" @default.
- W4284962597 title "The maximum spectral radius of graphs of given size with forbidden subgraph" @default.
- W4284962597 doi "https://doi.org/10.48550/arxiv.2207.03045" @default.
- W4284962597 hasPublicationYear "2022" @default.
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