Czechoslovak Mathematical Journal

, Volume 63, Issue 4, pp 909–922 | Cite as

Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

Article

Abstract

In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on n vertices with girth g (n, g being fixed), which graph minimizes the Laplacian spectral radius? Let Un,g be the lollipop graph obtained by appending a pendent vertex of a path on ng (n > g) vertices to a vertex of a cycle on g ⩾ 3 vertices. We prove that the graph Un,g uniquely minimizes the Laplacian spectral radius for n ⩾ 2g − 1 when g is even and for n ⩾ 3g − 1 when g is odd.

Keywords

Laplacian matrix Laplacian spectral radius girth unicyclic graph 

MSC 2010

05C50 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesNational Institute of Science Education and Research (NISER), P.O. Sainik SchoolBhubaneswarIndia

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