For a fixed integer $k\ge 2$, let $W_{2k+1}=K_1\vee C_{2k}$ be an odd wheel graph. The fixed-size spectral extremal problem aims to determine \[ \operatorname{spex}(m,W_{2k+1}):=\max\{\rho(G): e(G)=m,\ G \text{ is } W_{2k+1}\text{-free}\}, \] where $\rho(G)$ denotes the adjacency spectral radius. Based on this problem,...
For a fixed integer $k\ge 2$, let $kK_3$ denote the vertex-disjoint union of $k$ triangles. A recent fixed-size spectral theorem of Das and Yamini asserts that, for all sufficiently large $m$, every $kK_3$-free graph $G$ of size $m$ satisfies $\lambda(G)\le (k-1)+\sqrt{m-k(k-1)},$ and equality holds if and only if $(2k...
For a fixed integer $k\ge 2$, let $W_{2k+1}=K_1\vee C_{2k}$ be an odd wheel graph. The fixed-size spectral extremal problem aims to determine \[ \operatorname{spex}(m,W_{2k+1}):=\max\{\rho(G): e(G)=m,\ G \text{ is } W_{2k+1}\text{-free}\}, \] where $\rho(G)$ denotes the adjacency spectral radius. Based on this problem,...
Jing Gao, Xian-Ya Geng, Shu-Chao Li· 1 citation
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