Advances and Applications in Discrete Mathematics
Volume 4, Issue 1, Pages 17 - 23
(July 2009)
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TRIANGULAR LINE SIGNED GRAPH OF A SIGNED GRAPH
M. S. Subramanya (India) and P. Siva Kota Reddy (India)
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where
is a graph called the underlying graph of S and
is a function. The triangular line graph of a graph
is a graph
with vertex set
such that two vertices e and f are
adjacent if and only if the corresponding edges in G belong to a triangle of G. Analogously, we define the triangular line signed graph of a signed graph
as
a signed graph
where
is the underlying graph of
where for any edge
in
It is shown that for any signed
graph S, its triangular line signed graph
is balanced. Two signed graphs
and
are switching equivalent written
whenever there exists a marking m of
such that the signed graph
obtained by changing the sign of
every edge of
to its opposite whenever its end vertices are of opposite
signs, is isomorphic to
Further, a structural
characterization of signed graphs that are switching equivalent to their line
signed graphs is obtained.