On the signless Laplacian spectral radius of $C_4$-free $k$-cyclic graphs

Abstract

A $k$-cyclic graph is a connected graph of order $n$ and size $n+k-1$. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all $C_4$-free $k$-cyclic graphs of order $n$. Furthermore, we determine the first three unicyclic, and bicyclic, $C_4$-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the (combinatorial) Laplacian.

7 pages,3 figures

References in corpus (1)

• Maxima of the Q-index: forbidden even cycles