Year: 2026
Type: article
Abstract: This article characterizes the unicyclic graphs G with the following property: when a new edge with positive weight w is added between two non-adjacent vertices of G or when the weight of an existing edge is increased by w, exactly two Laplacian eigenvalues of G each increase by w, while all other eigenvalues remain unchanged. Furthermore, we identify the unicyclic graphs for which one of the altered eigenvalues is the algebraic connectivity.
Authors: Parameswar Basumatary, Debajit Kalita
Institutions: Salbari College, Tezpur University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7163535546