Alternative Proofs on the Indices of Cacti and Unicyclic Graphs with n Vertices

Authors

Sudipta Mallik, Marshall UniversityFollow

Document Type

Article

Publication Date

10-2011

Abstract

Let H_n be the cactus obtained from the star K_1,n—1 by adding _└ n—1/2_┘ independent edges between pairs of pendant vertices. Let K₁,⁺_n—1 be the unicyclic graph obtained from the star by appending one edge. In this paper we give alternative proofs of the following results: Among all cacti with n vertices, H_n is the unique cactus whose spectral radius is maximal, and among all unicyclic graphs with n vertices, K₁,⁺_n—1 is the unique unicyclic graph whose spectral radius is maximal. We also prove that among all odd-cycle graphs with n vertices, H_n is the unique odd-cycle graph whose spectral radius is maximal.

Comments

This is the author’s preprint available on arXiv at http://arxiv.org/abs/1110.2571.

Copyright © 2011 The Author. All rights reserved.

Recommended Citation

Mallik, S. (2011). Alternative Proofs on the Indices of Cacti and Unicyclic Graphs with n Vertices. arXiv preprint arXiv:1110.2571.