TY - JOUR
T1 - On (Semi-) Edge-primality of Graphs
TT -
JF - IJMSI
JO - IJMSI
VL - 12
IS - 2
UR - http://ijmsi.ir/article-1-924-en.html
Y1 - 2017
SP - 1
EP - 14
KW - Prime labeling
KW - Edge-prime labeling
KW - Semi-Edge-prime labeling
KW - Bipartite graphs
KW - Tripartite graphs.
N2 - 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.
M3 10.7508/ijmsi.2017.2.001
ER -