On Strongly *-Graphs: On Strongly *-Graphs

Mohamed Abdel-Azim  Seoud; Eliwa Mohamed  Roshdy; Mohamed Saied  AboShady

Authors

Mohamed Abdel-Azim Seoud Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, Egypt
Eliwa Mohamed Roshdy Department of Basic & Applied Sciences, Arab Academy of Science, Technology and Maritime Transport, Cairo, Egypt
Mohamed Saied AboShady Department of Engineering Physics and Mathematics, Faculty of Engineering, Ain Shams University, Cairo, Egypt

Keywords:

Strongly *-graph / labeling, C programming Language

Abstract

A graph ???????? = (????????, ????????) is said to be strongly *-graph if there exists a bijection ???????? ∶ ???????? → {1,2,…, ????????} in such a way that when an edge, whose vertices are labeled ???????? and ????????, is labeled with the value ???????? + ???????? + ????????????????, all edge labels are distinct. In this paper we get an upper bound for the number of edges of any graph with ???????? vertices to be strongly*- graph, and we make an algorithm to check any graph if it is a strongly*- graph or not. Also, we study some new families to be strongly*- graphs.

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On Strongly *-Graphs