Even Vertex Odd Mean Labeling of Graphs

Abstract

A graph with ???? vertices and ???? edges is said to have an even vertex odd mean labeling if there exits an injective function ????: ????(????) ⟶ { 0,2,4, … . , 2???? − 2,2????} such that the induced map ????∗: ????(????) ⟶ {1,3,5, … 2???? − 1} defined by ????∗(????????) = ????(????)+????(????) 2 is a bijection.
A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. Here we investigate the even vertex odd mean labeling of ???????????? (+)(???? ≥ 3) , Flag graph and other graphs.