On the relations among edge magic total, edge antimagic total, and ASD-antimagic graphs - Pancahayani, Sigit; Simanjuntak, Rinovia; Baca, Martin; Semanicova-Fenovcıkova, Andrea; Uttunggadewa, Saladin (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2025)
Let G be a simple and finite graph of order p and size q. The graph G is said to be edge magic total (EMT) if there is a bijection λ:V(G)∪E(G)→1,2,…,p+q such that all edge sums λ(x)+λ(xy)+λ(y), xy∈E(G), are the same. If all edge sums are pairwise distinct, then G is called edge antimagic total (EAT). Let t be a positive integer that satisfies C(t+1,2)≤q<C(t+2,2). The graph G is said to have an ascending subgraph decomposition (ASD) if G can be decomposed into t subgraphs H1,H2,…,Ht without isolated vertices such that Hi is isomorphic to a proper subgraph of Hi+1 for 1≤i≤t−1. A graph that admits an ascending subgraph decomposition is called an ASD graph. An ASD graph G is said to be ASD-antimagic if there exists a bijection f:V(G)∪E(G)→1,2,…,p+q such that all subgraph weights w(Hi)=∑v∈V(Hi)f(v)+∑e∈E(Hi)f(e), 1≤i≤t, are distinct. In this paper, we provide constructions of ASD-antimagic graphs arising from EMT or EAT graphs.