Balanced Cayley graphs and balanced planar graphs
نویسندگان
چکیده
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.
منابع مشابه
Regular maps from Cayley graphs, part 1: Balanced Cayley maps
Skoviera, M. and J. ‘&Iii, Regular maps from Cayley graphs, Part i: Balanced Cayley maps, Discrete Mathematics IO9 (1992) 265-276. A Cayley map is a Cayley graph 2-cell embedded in some orientable surface so that the local rotations at every vertex are identical. Two types of Cayley maps are introduced: the balanced and antibalanced Cayley maps. In Part 1, conditions are given uuder which a bal...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2010