Super Edge Magic Harmonious labeling for Certain Graphs

Document Type : Original Article

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Department of Mathematics, Faculty of Science, Suez University, Suez, Egypt

Abstract

Edge labelling of graphs has received a lot of attention in the last few years. Both graph theory, networks, and discrete mathematics are fields that are still interested in this area. It is yet uncertain for many graphs whether super edge magic harmonious labeling exists or not. A graph Γ=(V(Γ),E(Γ)) with P=∣V(Γ)∣ vertices and q=∣E(Γ)∣ edges, is called an edge bimagic harmonious graph if there exists a bijective mapping Ψ:[V(Γ)∪E(Γ)] →{1,2,3,⋯,p+q} such that for each edge xy∈E(Γ) , the value of the formula [(Ψ(x)+Ψ(y)) mod(q)+Ψ(xy)]=K_1 or K_2 , where K_i is a constant. If there exist three constants K_1 ,K_2 and K_3, it is said to be edge trimagic harmonious graph. We demonstrate in this study that the wheel graph W_n and the splitting graph of odd cycle are super edge bimagic harmonious graphs. Furthermore, we point out that the sunflower graph and the double sunflower graph are super edge trimagic harmonious graphs.

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