An algebraic approach for finding balance index sets

Wai Chee Shiu, Harris Kwong

Research output: Contribution to journalJournal articlepeer-review

11 Citations (Scopus)


Any vertex labeling f : V →{0,1} of the graph G = (V,E) induces a partial edge labeling f* : E → {0,1} defined by f*(uv)= f (u)if and only if f (u)= f (v). The balance index set of G is defined as {\f *-1 (0) - f| \f-1 (0) - f-1 (1) ≤1}. In this paper, we propose a new and easier approach to find the balance index set of a graph. This new method makes it possible to determine the balance index sets of a large number of families of graphs in an unified and uniform manner.

Original languageEnglish
Pages (from-to)139-155
Number of pages17
JournalAustralasian Journal of Combinatorics
Publication statusPublished - Oct 2009

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics


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