Characterization of a Signed Graph Whose Signed Line Graph is S-Consistent

Acharya, B. D. and Mukti Acharya, and Deepa Sinha, (2009) Characterization of a Signed Graph Whose Signed Line Graph is S-Consistent. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 32 (3). pp. 335-341.

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Abstract

A signed graph is a graph in which every edge is designated to be either positive or negative; it is balanced if every cycle contains an even number of negative edges. A marked signed graph is a signed graph each vertex of which is designated to be positive or negative and it is consistent if every cycle in the signed graph possesses all even number of negative vertices. Signed line graph L(S) of a given signed graph S = (G, sigma), as given by Behzad and Chartrand 7], is the signed graph with the standard line graph L(G) of G as its underlying graph and whose edges are assigned the signs according to the rule: for any e(i)e(j) is an element of E(L(S)), e(i)e(j) is an element of E(-) (L(S)) double left right arrow the edges e(i) and e(j) of S are both negative in S. Further, L(S) is S-consistent if to each vertex e of L(S), which is all edge of S, one assigns the sign sigma(e) then the resulting marked signed graph (L(S))mu is consistent. In this paper, we give a characterization of signed graphs S whose signed line graphs L(S) are S-consistent.

Item Type: Article
Uncontrolled Keywords: Balanced signed graph; consistent marked graph; signed line graph
Subjects: Physical Sciences > Mathematics
Divisions: PG Campuses > Manasagangotri, Mysore > Mathematics
Depositing User: Users 1 not found.
Date Deposited: 02 Apr 2013 11:41
Last Modified: 23 Aug 2013 11:20
URI: http://eprints.uni-mysore.ac.in/id/eprint/2842

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