Antimagic labelings on graphs with ascending subgraph decomposition

Pancahayani, Sigit; Simanjuntak, Rinovia; Uttunggadewa, Saladin

doi:10.22108/toc.2025.143242.2219

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	Antimagic labelings on graphs with ascending subgraph decomposition
Transactions on Combinatorics
دوره 15، شماره 4، اسفند 2026، صفحه 317-333 اصل مقاله (549.79 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.143242.2219
نویسندگان
Sigit Pancahayani¹؛ Rinovia Simanjuntak^* ²؛ Saladin Uttunggadewa²
¹Doctoral Program in Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia
²Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia
چکیده
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 $1 \leq i \leq t-1$. 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. 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.
کلیدواژه‌ها
ascending subgraph decomposition (ASD)؛ antimagic labeling؛ $(a؛ d)$-ASD antimagic labeling

مراجع
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Antimagic labelings on graphs with ascending subgraph decomposition