Volume 12, Issue 2 (9-2017)                   IJMSI 2017, 12(2): 1-14 | Back to browse issues page

DOI: 10.7508/ijmsi.2017.2.001

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Shiu W, Lau G, Lee S. On (Semi-) Edge-primality of Graphs. IJMSI. 2017; 12 (2) :1-14
URL: http://ijmsi.ir/article-1-924-en.html


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.

Type of Study: Research | Subject: Special

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