Balanced group-labeled graphs

6Citations
Citations of this article
7Readers
Mendeley users who have this article in their library.

Abstract

A group-labeled graph is a graph whose vertices and edges have been assigned labels from some abelian group. The weight of a subgraph of a group-labeled graph is the sum of the labels of the vertices and edges in the subgraph. A group-labeled graph is said to be balanced if the weight of every cycle in the graph is zero. We give a characterization of balanced group-labeled graphs that generalizes the known characterizations of balanced signed graphs and consistent marked graphs. We count the number of distinct balanced labellings of a graph by a finite abelian group Γ and show that this number depends only on the order of Γ and not its structure. We show that all balanced labellings of a graph can be obtained from the all-zero labeling using simple operations. Finally, we give a new constructive characterization of consistent marked graphs and markable graphs, that is, graphs that have a consistent marking with at least one negative vertex. © 2011 Elsevier B.V. All rights reserved.

Cite

CITATION STYLE

APA

Joglekar, M., Shah, N., & Diwan, A. A. (2012). Balanced group-labeled graphs. Discrete Mathematics, 312(9), 1542–1549. https://doi.org/10.1016/j.disc.2011.09.021

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free