:: Volume 12, Number 2 (9-2017) ::
IJMSI 2017, 12(2): 1-14 Back to browse issues page
On (Semi-) Edge-primality of Graphs
W.-C. Shiu, G.-C. Lau , S.-M. Lee

Let $G= (V,E)$ be a $(p,q)$-graph. A bijection $f: Eto{1,2,3,ldots,q }$ is called an edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ where $f^+(u) = sum_{uwin E} f(uw)$. Moreover, a bijection $f: Eto{1,2,3,ldots,q }$ is called a semi-edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ or $f^+(u)=f^+(v)$. A graph that admits an  edge-prime (or a semi-edge-prime) labeling is called an edge-prime (or a semi-edge-prime) graph. In this paper we determine the necessary and/or sufficient condition for the existence of (semi-) edge-primality of many family of graphs.

Keywords: Prime labeling, Edge-prime labeling, Semi-Edge-prime labeling, Bipartite graphs, Tripartite graphs.
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Type of Study: Research | Subject: Special

DOI: 10.7508/ijmsi.2017.2.001

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Volume 12, Number 2 (9-2017) Back to browse issues page