Super H-Antimagic Total Covering for Generalized Antiprism and Toroidal Octagonal Map. (9th August 2021) - Taimur, Amir; Ali, Gohar; Numan, Muhammad; Aslam, Adnan; Yannick, Kraidi Anoh
Abstract : Let G be a graph and H ⊆ G be subgraph of G . The graph G is said to be a, d -H antimagic total graph if there exists a bijective function f : V H ∪ E H ⟶ 1, 2, 3, …, V H + E H such that, for all subgraphs isomorphic to H, the total H weights W H = W H = ∑ x ∈ V H f x + ∑ y ∈ E H f y forms an arithmetic sequence a, a + d, a + 2 d, …, a + n − 1 d, where a and d are positive integers and n is the number of subgraphs isomorphic to H . An a, d -H antimagic total labeling f is said to be super if the vertex labels are from the set 1, 2, …, | V G . In this paper, we discuss super a, d -C 3 -antimagic total labeling for generalized antiprism and a super a, d -C 8 -antimagic total labeling for toroidal octagonal map.