2990 PRIME AVERAGE HARMONIOUS LABELING OF GRAPHS

Abstract

In this article study, we have presented innovative harmonious labeling as prime Average Harmonious Labeling of the graph . A function ???? is called prime average harmonious labeling of graph ???? with ???? vertices and ???? edges if ???? ∶ ???? → {0,1,2,3 … … . ,2???? − 1} is injective and the induced function ????∗ ∶ ????(????) → {0,1,2, … .2????} is defined by ????∗( ????????) = (i) ???????????? (????(????), ????(????)) = 1 , (ii) L(????????) = ????(????)+????(????)+1 2 (???????????? ????) ???????? ????(????) + ????(????) ???????? ???????????? , (iii)????(????????) = ????(????)+????(????) 2 (???????????? ????) ???????? ????(????) + ????(????) ???????? ????????????????.A graph that satisfies the above three conditionsare called a prime average harmonious labeling. A graph that admits a prime average harmonious labeling is called a prime average harmonious graph.