Reddy, P., Misra, U. (2013). Directionally $n$-signed graphs-III: the notion of symmetric balance. Transactions on Combinatorics, 2(4), 53-62.

P.Siva Kota Reddy; U. K. Misra. "Directionally $n$-signed graphs-III: the notion of symmetric balance". Transactions on Combinatorics, 2, 4, 2013, 53-62.

Reddy, P., Misra, U. (2013). 'Directionally $n$-signed graphs-III: the notion of symmetric balance', Transactions on Combinatorics, 2(4), pp. 53-62.

Reddy, P., Misra, U. Directionally $n$-signed graphs-III: the notion of symmetric balance. Transactions on Combinatorics, 2013; 2(4): 53-62.

Directionally $n$-signed graphs-III: the notion of symmetric balance

^{1}Dept. of Mathematics, Siddaganga Institute of Technology, B.H.Road,Tumkur-572103, India.

^{2}Berhampur University

Abstract

Let $G=(V, E)$ be a graph. By \emph{directional labeling (or d-labeling)} of an edge $x=uv$ of $G$ by an ordered $n$-tuple $(a_1,a_2,\dots,a_n)$, we mean a labeling of the edge $x$ such that we consider the label on $uv$ as $(a_1,a_2,\dots,a_n)$ in the direction from $u$ to $v$, and the label on $x$ as $(a_{n},a_{n-1},\dots,a_1)$ in the direction from $v$ to $u$. In this paper, we study graphs, called \emph{(n,d)-sigraphs}, in which every edge is $d$-labeled by an $n$-tuple $(a_1,a_2,\dots,a_n)$, where $a_k \in \{+,-\}$, for $1\leq k \leq n$. In this paper, we give different notion of balance: symmetric balance in a $(n,d)$-sigraph and obtain some characterizations.

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