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Directionally $n$-signed graphs-III: the notion of symmetric balance | ||
| Transactions on Combinatorics | ||
| مقاله 5، دوره 2، شماره 4، اسفند 2013، صفحه 53-62 اصل مقاله (348.87 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2013.3658 | ||
| نویسندگان | ||
| P.Siva Kota Reddy* 1؛ U. K. Misra2 | ||
| 1Dept. of Mathematics, Siddaganga Institute of Technology, B.H.Road,Tumkur-572103, India. | ||
| 2Berhampur University | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Signed graphs؛ Directional labeling؛ Complementation؛ Balance | ||
| مراجع | ||
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