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Directionally 2-Signed and Bidirected Graphs | | E. Sampathkumar
; M. A. Sriraj
; Thomas Zaslavsky
; | | Date: |
13 Mar 2013 | | Abstract: | An edge uv in a graph Gamma is directionally 2-signed (or, (2,d)-signed) by
an ordered pair (a,b), a,b in {+,-}, if the label l(uv) = (a,b) from u to v,
and l(vu) = (b,a) from v to u. Directionally 2-signed graphs are equivalent to
bidirected graphs, where each end of an edge has a sign. A bidirected graph
implies a signed graph, where each edge has a sign. We extend a theorem of
Sriraj and Sampathkumar by proving that the signed graph is antibalanced (all
even cycles and only even cycles have positive edge sign product) if, and only
if, in the bidirected graph, after suitable reorientation of edges every vertex
is a source or a sink. | | Source: | arXiv, 1303.3084 | | Services: | Forum | Review | PDF | Favorites | |
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