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Balanced group-labeled graphs

DSpace at IIT Bombay

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Title Balanced group-labeled graphs
 
Creator JOGLEKAR, M
SHAH, N
DIWAN, AA
 
Subject Group-labeled graphs
Signed graphs
Marked graphs
Balanced labellings
Fundamental cycles
Vertex switching
Markable graphs
CONSISTENT MARKED GRAPHS
 
Description 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 Gamma and show that this number depends only on the order of Gamma 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. (C) 2011 Elsevier B.V. All rights reserved.
 
Publisher ELSEVIER SCIENCE BV
 
Date 2014-10-16T12:28:36Z
2014-10-16T12:28:36Z
2012
 
Type Article; Proceedings Paper
 
Identifier DISCRETE MATHEMATICS, 312(9)1542-1549
http://dx.doi.org/10.1016/j.disc.2011.09.021
http://dspace.library.iitb.ac.in/jspui/handle/100/15547
 
Language en