2990 PRIME AVERAGE HARMONIOUS LABELING OF GRAPHS (International Journal of Food and Nutritional Sciences, 2022)
In this article study, we have presented innovative harmonious labeling as prime AverageHarmonious Labeling of the graph . A function ???? is called prime average harmonious labeling ofgraph ???? with ???? vertices and ???? edges if ???? ∶ ???? → {0,1,2,3 … … . ,2???? − 1} is injective and theinduced function ????∗ ∶ ????(????) → {0,1,2, … .2????} is defined by ????∗( ????????) =(i) ???????????? (????(????), ????(????)) = 1 , (ii) L(????????) =????(????)+????(????)+12(???????????? ????) ???????? ????(????) + ????(????) ???????? ???????????? ,(iii)????(????????) =????(????)+????(????)2(???????????? ????) ???????? ????(????) + ????(????) ???????? ????????????????.A graph that satisfies the above threeconditionsare called a prime average harmonious labeling. A graph that admits a prime averageharmonious labeling is called a prime average harmonious graph.