The Laplacian spectral radius of bicyclic graphs with a given girth

Authors:
Mingqing Zhai;Guanglong Yu;Jinlong Shu
Affiliations:
Department of Mathematics, East China Normal University, Shanghai, 200241, China and Department of Mathematics, Chuzhou University, Anhui, Chuzhou, 239012, China;Department of Mathematics, East China Normal University, Shanghai, 200241, China;Department of Mathematics, East China Normal University, Shanghai, 200241, China and Key Laboratory of Geographic Information Science, Ministry of Education East China Normal University, Shanghai, ...
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 2
Cited 0

On the spectral radius of complementary acyclic matrices of zeros and ones

SIAM Journal on Algebraic and Discrete Methods
The Laplacian spectrum of a graph

SIAM Journal on Matrix Analysis and Applications

Quantified Score

Hi-index	0.11

Visualization

Abstract

Let @?(n,g) be the class of bicyclic graphs on n vertices with girth g. Let @?"1(n,g) be the subclass of @?(n,g) consisting of all bicyclic graphs with two edge-disjoint cycles and @?"2(n,g)=@?(n,g)@?@?"1(n,g). This paper determines the unique graph with the maximal Laplacian spectral radius among all graphs in @?"1(n,g) and @?"2(n,g), respectively. Furthermore, the upper bound of the Laplacian spectral radius and the extremal graph for @?(n,g) are also obtained.