Maximizing the spectral radius of graphs of given size with forbidden a subgraph
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916199382646784 |
|---|---|
| author | Zhang, Yanting Wang, Ligong |
| author_facet | Zhang, Yanting Wang, Ligong |
| contents | Let $H_7$ denote the $7$-vertex \textit{fan graph} consisting of a $6$-vertex path plus a vertex adjacent to each vertex of the path. Let $K_3 \vee \frac{m-3}{3}K_1$ be the graph obtained by joining each vertex of a triangle $K_3$ to $\frac{m-3}{3}$ isolated vertices. In this paper, we show that if $G$ is an $H_{7}$-free graph with size $m\geq 33$, then the spectral radius $ ρ(G)\leq 1+\sqrt{m-2},$ equality holds if and only if $G\cong K_3 \vee \frac{m-3}{3}K_1$ (possibly, with some isolated vertices). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximizing the spectral radius of graphs of given size with forbidden a subgraph Zhang, Yanting Wang, Ligong Combinatorics Let $H_7$ denote the $7$-vertex \textit{fan graph} consisting of a $6$-vertex path plus a vertex adjacent to each vertex of the path. Let $K_3 \vee \frac{m-3}{3}K_1$ be the graph obtained by joining each vertex of a triangle $K_3$ to $\frac{m-3}{3}$ isolated vertices. In this paper, we show that if $G$ is an $H_{7}$-free graph with size $m\geq 33$, then the spectral radius $ ρ(G)\leq 1+\sqrt{m-2},$ equality holds if and only if $G\cong K_3 \vee \frac{m-3}{3}K_1$ (possibly, with some isolated vertices). |
| title | Maximizing the spectral radius of graphs of given size with forbidden a subgraph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.06843 |