On the Signless Laplacian Spectral Radius of C4-free k-cyclic Graphs

KONG Qi, WANG Li-gong

doi:10.13371/j.cnki.chin.q.j.m.2017.03.002

Chinese Quarterly Journal of Mathematics >

2017 , Vol. 32 >Issue 3: 238 - 245

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.03.002

On the Signless Laplacian Spectral Radius of C₄-free k-cyclic Graphs

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Departmant of Applied Mathematics, School of Science, Northwestern Polytechnical University

KONG Qi(1991-), female, native of Jincheng, Shanxi, a postgraduate student of Northwestern Polytechnical University, engages in graph theory and its application; WANG Li-gong(corresponding author)(1968-), male, native of Xinzhou, Shanxi, a professor of Northwestern Polytechnical University, Ph.D.,engages in graph theory and its applications.

Received date: 2016-12-23

Online published: 2020-10-21

Supported by

Supported by the National Natural Science Foundation of China(11171273)； Supported by the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(Z2016170)；

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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 C₄-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C₄-free graphs whose spectral radius of the signless Laplacian is maximal. Similar resultsare obtained for the（combinatorial） Laplacian

Key words： k-cyclic graph; C₄-free; signless Laplacian spectral radius; Laplacian spectral radius

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KONG Qi, WANG Li-gong . On the Signless Laplacian Spectral Radius of C₄-free k-cyclic Graphs[J]. Chinese Quarterly Journal of Mathematics, 2017 , 32(3) : 238 -245 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.03.002

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