TY - JOUR
T1 - On (Semi-) edge-primality of graphs
AU - Shiu, Wai Chee
AU - Lau, Gee Choon
AU - Lee, Sin Min
N1 - Publisher Copyright:
© 2017 Academic Center for Education, Culture and Research TMU.
PY - 2017/9
Y1 - 2017/9
N2 - Let G= (V,E) be a (p,q)-graph. A bijection f: E → to{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) =Σuw ∈Ef(uw). Moreover, a bijection f: E → {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.
AB - Let G= (V,E) be a (p,q)-graph. A bijection f: E → to{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) =Σuw ∈Ef(uw). Moreover, a bijection f: E → {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.
KW - Bipartite graphs
KW - Edge-prime labeling
KW - Prime labeling
KW - Semi-Edge-prime labeling
KW - Tripartite graphs
UR - http://www.scopus.com/inward/record.url?scp=85029743624&partnerID=8YFLogxK
U2 - 10.7508/ijmsi.2017.2.001
DO - 10.7508/ijmsi.2017.2.001
M3 - Journal article
AN - SCOPUS:85029743624
SN - 1735-4463
VL - 12
SP - 1
EP - 14
JO - Iranian Journal of Mathematical Sciences and Informatics
JF - Iranian Journal of Mathematical Sciences and Informatics
IS - 2
ER -