Czechoslovak Mathematical Journal

, Volume 63, Issue 4, pp 909–922

# 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

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