Abstract

Graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. A graph G=(V,E) with p vertices and q edges is said to admit Lehmer-3 mean cordial labeling if the mapping h from V(G) to {1,2,3} induces the mapping h^* from E(G) to {1,2,3} as h^* (xy)=?(?h(x)?^3+?h(y)?^3)/(?h(x)?^2+?h(y)?^2 )? with the condition that the number of vertices labeled with i and the number of vertices labeled with j differ at most by 1, the number of edges labeled with i and the number of edges labeled with j differ at most by 1 where i,j?{1,2,3}. A graph with a Lehmer-3 mean cordial labeling is called a Lehmer-3 mean cordial graph. In this paper, we prove that all trees, cycle graph C_n (n?1,2(mod 3)), pinwheel graph ?PW?_n, armed crown graph ?AC?_(m,n ), the graphs L_n?K_1 and ?CL?_n?K_1 are Lehmer-3 mean cordial graphs

Description