On the signless Laplacian spectral radius of $C_{4}$-free $k$-cyclic graphs

DOI10.13371/J.CNKI.CHIN.Q.J.M.2017.03.002zbMATH Open1424.05186arXiv1612.03538MaRDI QIDQ4623804

Qi Kong, Li-Gong Wang

Publication date: 22 February 2019

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.

Full work available at URL: https://arxiv.org/abs/1612.03538

zbMATH Keywords

signless Laplacian spectral radius\(k\)-cyclic graph\({C_4}\)-free

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Connectivity (05C40)

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