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Paper Information

Journal:   TRANSACTIONS ON COMBINATORICS   2014 , Volume 3 , Number 4; Page(s) 11 To 18.
 
Paper: 

ON LICT SIGRAPHS

 
 
Author(s):  MATHAD V.*, NARAYANKAR K.P.
 
* DEPARTMENT OF STUDIES IN MATHEMATICS, UNIVERSITY OF MYSORE, MYSORE, INDIA
 
Abstract: 

A signed graph (marked graph) is an ordered pair S= (G, s) (S= (G, m)), where G= (V, E) is a graph called the underlying graph of S and s: E ® {+,-} (m: V® {+,-}) is a function. For a graph G, V (G), E (G) and C (G) denote its vertex set, edge set and cut-vertex set, respectively. The lict graph Lc (G) of a graph G= (V, E) is defined as the graph having vertex set E (G) E C (G) in which two vertices are adjacent if and only if they correspond to adjacent edges of G or one corresponds to an edge ei of G and the other corresponds to a cut-vertex cj of G such that ei is incident with cj. In this paper, we introduce lict sigraphs, as a natural extension of the notion of lict graph to the realm of signed graphs. We show that every lict sigraph is balanced. We characterize signed graphs S and S' for which S ~ Lc (S), h (S) ~ Lc (S), L (S) ~ Lc (S'), J (S) ~ Lc (S') and T1 (S) ~ Lc (S'), where h (S), L (S), J (S) and T1 (S) are negation, line graph, jump graph and semitotal line sigraph of S, respectively, and ~ means switching equivalence.

 
Keyword(s): SIGNED GRAPH, LINE SIGRAPH, JUMP SIGRAPH, SEMITOTAL LINE SIGRAPH, LICT SIGRAPH
 
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