Let $kK_{r+1}$ be the graph consisting of $k$ vertex-disjoint copies of the complete graph $K_{r+1}$. Moon [Canad. J. Math. 20 (1968) 95--102] and Simonovits [Theory of Graphs (Proc. colloq., Tihany, 1996)] independently showed that if $n$ is sufficiently large, then the join of a complete graph $K_{k-1}$ and an $r$-partite Turán graph $T_{n-k+1,r}$ is the unique extremal graph for $kK_{r+1}$. In this paper we consider the graph which has the maximum spectral radius among all graphs without $k$ disjoint cliques. We show that if $G$ attains the maximum spectral radius over all $n$-vertex $kK_{r+1}$-free graphs for sufficiently large $n$, then $G$ is isomorphic to the join of a complete graph $K_{k-1}$ and an $r$-partite Turán graph $T_{n-k+1,r}$.
@article{10_37236_11516,
author = {Zhenyu Ni and Jing Wang and Liying Kang},
title = {Spectral extremal graphs for disjoint cliques},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {1},
doi = {10.37236/11516},
zbl = {1512.05280},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11516/}
}
TY - JOUR
AU - Zhenyu Ni
AU - Jing Wang
AU - Liying Kang
TI - Spectral extremal graphs for disjoint cliques
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/11516/
DO - 10.37236/11516
ID - 10_37236_11516
ER -
%0 Journal Article
%A Zhenyu Ni
%A Jing Wang
%A Liying Kang
%T Spectral extremal graphs for disjoint cliques
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/11516/
%R 10.37236/11516
%F 10_37236_11516
Zhenyu Ni; Jing Wang; Liying Kang. Spectral extremal graphs for disjoint cliques. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11516
