On certain associated graphs of set-valued signed graphs

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Authors :

P.K. Ashraf 1 , K.A. Germina 2 and N.K. Sudev 3 *

Author Address :

1 Department of Mathematics, Government Arts and Science College, Kondotty, Kerala, India.
2 Department of Mathematics, Central University of Kerala, Kasaragod, Kerala, India.
3 Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka, India.

*Corresponding author.

Abstract :

Let $X$ be a non-empty set and let $S$ be a signed graph, with corresponding underlying graph $G$ and the signature $s$. An injective function $f:V(S) o cP(X)$ is said to be a set-labeling of $S$ if $f$ is a set-labeling of the underlying graph $G$ and the signature of $S$ is defined by $s(uv)=(-1)^{|f(u)oplus f(v)|}$. A signed graph $S$ together with a set-labeling $f$ is known as a set-labeled signed graph and is denoted by $S_f$. In this paper, we discuss the characteristics of certain signed graphs associated with given set-valued signed graphs.

Keywords :

Signed graphs, balanced signed graphs, set-valuations of signed graphs.



Article Info :

Received : June 27, 2018; Accepted : January 25, 2019.



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