Graph labeling plays an important role in many fields such as computer science, coding theory, astronomy and physics. Bača, in [1] introduced, for an undirected, simple and connected graph G , the definition of an edge iirregular itotal π-labeling H:V(G) ∪ E(G)→{ 1,2,3,…,π} which is a labeling of its edges and vertices in such a way that any two edges rm and r^* m^* in G have different weights, i.e.〖 w〗_H (rm)≠w_H (r^* m^* ) where w_H (rm)=H(rm)+H(r)+H(m). The bound of TEIS for any graph G .,with maximum degree ∆G , is given in the following inequality

tes(G)≥max{⌈(∆G+1)/2⌉,⌈(|E(G)|+2)/3⌉ } Conjecture 1. For any graph G different from K_5,we have

tes(G)=max{⌈(∆G+1)/2⌉,⌈(|E(G)|+2)/3⌉}.



In this paper, we introduce definitions for two kinds of graphs: a bee snake graph 〖BS〗_n and a double bee snake graph D(〖BS〗_n ). The exact values of total edge irregularity strength (TEIS) for the new graphs have also been determined.