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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  B n ( C 3, 5, 7, …2 n +1 ) and even arithmetic book graph  B n ( C 4, 6, 8 , …,  2 n +2 ) of  n  sheets. We found that the  tes  of odd arithmetic book graph  B n ( C 3, 5, 7 , …,  2 n +1 ) of  n  sheets is equal to the ceiling function of    n 2 + n + 3 3 and the  tes  of even arithmetic book graph  B n ( C 4, 6, 8 , …,  2 n +2 ) is equal to the ceiling function of    n 2 + 2 n + 3 3 .

Total Edge Irregularity Strength of Arithmetic Book Graphs