ON STRONGLY ∗-GRAPHS AND STRONGLY MULTIPLICATIVE GRAPHS

ON STRONGLY ∗-GRAPHS AND STRONGLY MULTIPLICATIVE GRAPHS

M. M. Farid, A. E. A. Mahran, M. Anwar, M. A. Seoud

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Abstract

This paper studies strongly ∗-graphs as a variation of strongly multiplicative graphs. We show that every strongly multiplicative graph induces a strongly ∗-graph. We establish a relationship between the upper bounds on the number of edges of strongly ∗-graphs λ∗(n) and strongly multiplicative graphs, and identify a condition under which the upper bound for strongly ∗-graphs exceeds that of strongly multiplicative graphs, we show that this condition holds for infinitely many values of n. We derive explicit formulas for λ∗(n). Finally, we prove the independence of several necessary conditions for graphs that do not admit strongly∗-labeling.

Keywords

strongly ∗-graphs, strongly multiplicative, Graph labeling.