University of Isfahan Transactions on Combinatorics 2251-8657 15 4 2026 12 01 Antimagic labelings on graphs with ascending subgraph decomposition 317 333 29813 10.22108/toc.2025.143242.2219 EN Sigit Pancahayani Doctoral Program in Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia Rinovia Simanjuntak Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia 0000-0002-3224-2376 Saladin Uttunggadewa Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia Journal Article 2024 10 31 Let $t$ and $q$ be positive integers that satisfy $\binom{t+1}{2} \leq q< \binom{t+2}{2}$ and $G$ be a simple and finite graph of size $q$. $G$ is said to be an ascending subgraph decomposition (ASD) graph if $G$ can be decomposed into $t$ subgraphs $H_1, H_2,\ldots,H_t$ without isolated vertices such that $H_i$ is isomorphic to a proper subgraph of $H_{i+1}$, for $1 \leq i \leq t-1$.<br /> <br />In this paper, we introduce a new type of antimagic labeling based on the notion of ASD. Let $G$ be an ASD graph and $f:V(G)\cup E(G) \rightarrow \{1,2,\ldots,\lvert V(G)\rvert+\lvert E(G)\rvert\}$ a bijection. The weight of a subgraph $H_i$ $(1\leq i\leq t)$ is $w(H_i)=\sum_{v\in V(H_i)}f(v)+\sum_{e\in E(H_i)}f(e)$. If the weights of all $H_i$s $(1\leq i\leq t)$ form an arithmetic progression with the smallest weight $a$ and common difference $d$, then $f$ is called an $(a,d)$-ASD antimagic labeling and $G$ is an $(a,d)$-ASD antimagic graph.<br /> <br />We provide an upper bound for $d$ in an $(a,d)$-ASD antimagic graph. We define and utilize the $(t,\delta)$-ascending antibalanced multisets to label some product graphs, including disjoint union, vertex amalgamation, edge amalgamation, subgraph amalgamation, and extended chain of graphs. https://toc.ui.ac.ir/article_29813_0ecf599d969a776a35604a8322cfc501.pdf