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Parity Labeling in Signed Graphs
- Source :
- Journal of Prime Research in Mathematics, 17(2) (2021), 1-7
- Publication Year :
- 2020
-
Abstract
- Let $S=(G, \sigma)$ be a signed graph where $G=(V, E)$ is a graph called the underlying graph of $S$ and $\sigma:E(G) \rightarrow \{+,~-\}$. Let $f:V(G) \rightarrow \{1,2,\dots,|V(G)|\}$ such that $\sigma(uv)=+$ if and only if $f(u)$ and $f(v)$ are of same parity and $\sigma(uv)=-$ if and only if $f(u)$ and $f(v)$ are of opposite parity. Under $f$ we get a signed graph $G_f$ denoted as $S$, which is a parity signed graph. In this paper, we initiate the study of parity labeling in signed graphs and we define and find `rna' number denoted as $\sigma^-(S)$ for some classes of signed graphs. We also characterize some signed graphs which are parity signed graphs. Some directions for further research are also suggested.<br />Comment: 10 pages, 1 figure
- Subjects :
- Mathematics - Combinatorics
05C22, 05C75
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Prime Research in Mathematics, 17(2) (2021), 1-7
- Publication Type :
- Report
- Accession number :
- edsarx.2012.07737
- Document Type :
- Working Paper