Balanced Cayley graphs and balanced planar graphs

Details Balanced Cayley graphs and balanced planar graphs Balanced Cayley graphs and balanced planar graphs

2007-07-02

arxiv.org/abs/0707.0155v1

Mathematics

Combinatorics

Scientific paper

A balanced graph is a bipartite graph with no induced circuit of length 2 mod 4. These graphs arise in linear programming. We focus on graph-algebraic properties of balanced graphs to prove a complete classification of balanced Cayley graphs on abelian groups. Moreover, in Section 5 of this paper, we prove that there is no cubic balanced planar graph. Finally, some remarkable conjectures for balanced regular graphs are also presented.

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