Total Edge Irregularity Strength of Arithmetic Book Graphs

Abstract

For any simple undirected graph G(V, E), a map f : V ⋃ E → {1, 2, …, k} such that for any different edges xy and x’y’ their weights are distinct is called an edge irregular total k-labeling. The weight of edge xy is defined as the sum of edge label of xy, vertex label of x and vertex label of y. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G and is denoted by tes(G). In this paper, we determine the exact value of the total edge irregularity strength of odd arithmetic book graph Bn (C 3, 5, 7, …2n+1) and even arithmetic book graph Bn (C 4, 6, 8, …, 2n+2) of n sheets. We found that the tes of odd arithmetic book graph Bn (C 3, 5, 7, …, 2n+1) of n sheets is equal to the ceiling function of n 2 + n + 3 3 and the tes of even arithmetic book graph Bn (C 4, 6, 8, …, 2n+2) is equal to the ceiling function of n 2 + 2 n + 3 3 .

Total edge irregularity strength of quadruplet and quintuplet book graphs

“…( We have defined the edge labelling for the first book, the second book and the third book in [20]. We prove the edge labelling of the fourth book for three different cases.…”

“…Research on the of cyclic graphs for various graph classes is still being done. Several studies on the exact value of in some cyclic graphs, including some book graphs, have been conducted by [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…In previous research [20], we have shown the of triple book graphs, and we have constructed the formula of an edge irregular total k-labelling of the first book, the second book and the third book. The results, the first book, the second book and the third book have *Corresponding author: ratnasari.lucia@gmail.com different edge labelling formulas.…”

Some Cartesian Products of a Path and Prism Related Graphs That Are Edge Odd Graceful

“…are mentioned in the survey. And for those mentioned labeling, many classes of graphs have been investigated, for instance in [1], [2], [4], [5], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. One other labeling called edge odd graceful labeling is also introduced, by Solairaju et.all [16].…”

On Total Edge Irregularity Strength of Staircase Graphs and Related Graphs

“…In [7] and [8], Putra, et al observed the tes of centralized uniform theta graphs and the tes of uniform theta graphs, respectively. In [9] and [10], Ratnasari, et al gave the exact value of the tes of some ladder related graphs and arithmetic book graphs, respectively.…”