1. Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth
- Creator:
- Patra, Kamal Lochan and Sahoo, Binod Kumar
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Laplacian matrix, Laplacian spectral radius, girth, and unicyclic graph
- Language:
- English
- Description:
- 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 $U_{n,g}$ be the lollipop graph obtained by appending a pendent vertex of a path on $n-g$ $(n> g)$ vertices to a vertex of a cycle on $g\geq 3$ vertices. We prove that the graph $U_{n,g}$ uniquely minimizes the Laplacian spectral radius for $n\geq 2g-1$ when $g$ is even and for $n\geq 3g-1$ when $g$ is odd.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public