Edges and vertices in a unique signed circle in a signed graph. Issue 3 (1st December 2017)

• Record Type: Journal Article
• Authors: Behr, Richard
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 14:Issue 3(2017)
• Page Start: 224
• Page End: 232
• Publication Date: 2017-12-01
• Subjects: Signed graph -- Balance -- Negative circle -- Positive circle -- Bridge
• DOI: 10.1016/j.akcej.2017.03.004
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: We examine the conditions under which a signed graph contains an edge or a vertex that is contained in a unique negative circle or a unique positive circle. For an edge in a unique signed circle, the positive and negative case require the same structure on the underlying graph, but the requirements on the signature are different. We characterize the structure of the underlying graph necessary to support such an edge in terms of bridges of a circle. We then use the results from the edge version of the problem to help solve the vertex version.