Indian Journal of Science and Technology
DOI: 10.17485/ijst/2020/v13i02/148783
Year: 2020, Volume: 13, Issue: 2, Pages: 141 – 148
Original Article
Sunoj B.S.*,1 and Mathew Varkey T.K.2
1Department of Mathematics, Government Polytechnic College, Attingal, Kerala, India
2Department of Mathematics, TKM College of Engineering, Kollam, Kerala, India
*Author for correspondence:
B.S. Sunoj
Department of Mathematics, Government Polytechnic College, Attingal, Kerala, India
E-mail ID: spalazhi@yahoo.com
Objectives: Our aim is to find new families of di graphs that admit linear incidence edge prime labeling.
Methods/statistical analysis: Here the vertices are assigned with 0,1,…,m−1 and edges with 2g(v) + g(u), where u is the initial vertex and v is the terminal vertex and g is the vertex labeling function. The graph is prime when the greatest common incidence number of vertices with in degree greater than one is one.
Findings: Here we prove that di graph of corona product of Pn with K2, strong shadow graph of path Pn, strong splitting graph of path Pn, square graph of path Pn, tortoise graph of path Pn, graph obtained by joining the corresponding internal vertices of two copies of path Pn, strong Z graph of path Pn admit linear incidence edge prime labeling.
Application/improvements: One can generalize these results and find some structural properties. These results may be applied to the transportation problem, chemical graph theory and decision analysis.
Keywords: Linear, Incidence, Prime Labeling, Strong Z Graph of Path Pn, Strong Shadow Graph of Path Pn, Strong Splitting Graph of Path Pn.
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