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Balance in gain graphs – A spectral analysis
- Source :
-
Linear Algebra & its Applications . Mar2012, Vol. 436 Issue 5, p1114-1121. 8p. - Publication Year :
- 2012
-
Abstract
- Abstract: A gain graph is a graph where the edges are given some orientation and labeled with the elements (called gains) from a group so that gains are inverted when we reverse the direction of the edges. A signed graph with labels from the multiplicative group on the edges can be taken as a particular case of a gain graph. In this article, we initiate a matrix analysis of gain graphs by defining the adjacency matrices of gain graphs when the underlying group for labeling the edges is the multiplicative group of a field and characterize balance in such gain graphs using the characteristic polynomials. We also establish recurrence relations for the characteristic polynomials of a gain graph and discuss consequences of these relations. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 436
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 70392441
- Full Text :
- https://doi.org/10.1016/j.laa.2011.07.005