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The Laplacian spectral radius of bicyclic graphs with a given girth

✍ Scribed by Mingqing Zhai; Guanglong Yu; Jinlong Shu

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
622 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis

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

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