Domination number and (signless Laplacian) spectral radius of cactus graphs

Abstract

A cactus graph is a connected graph whose block is either an edge or a cycle. A vertex set $S\subseteq V(G)$ is said to be a dominating set of a graph $G$ if every vertex in $V(G)\setminus S$ is adjacent to a vertex in $S$. There are several results on the (signless Laplacian) spectral radius and domination number in graph theory. In this paper, we determine the unique graph with the maximum adjacency spectral radius and signless Laplacian spectral radius among all cactus graphs with fixed domination number.