Signed Distance in Signed Graphs

Abstract

Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae for the distance spectrum of some unbalanced signed graphs. We also introduce the notion of distance-compatible signed graphs and partially characterize it.

arXiv commentv1: 11 pp. v2: 16 pp with more eigenvalue results and 2 figures