Bee Snake Graph and Its Total Edge Irregularity Strength | ||
| Delta Journal of Science | ||
| Volume 48, Issue 2, August 2024, Pages 39-55 PDF (1.45 M) | ||
| Document Type: Research and Reference | ||
| DOI: 10.21608/djs.2024.287214.1164 | ||
| Authors | ||
| Fatma Salama* 1; Hala Attiya2 | ||
| 1Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt | ||
| 2Basic Science Department, Faculty of Technology and Education, Beni-Suef University, Beni-Suef | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Total edge irregularity strength; Irregular labelling; Edge irregular total labeling; Bee snake graph | ||
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