Inclusive Distance Antimagic Labeling of Shadow Graph of Complete and Circulant Graph

Arafah, Siti Hafshah Nurul
Sugeng, Kiki Ariyanti
Haryeni, Debi Oktia

Jurnal Matematika UNAND
Vol. 15 No. 1 (2026)

Consider a graph $G = (V, E)$ with order $n$. Suppose that we have a bijection $f: V(G) \to \{1, 2, ..., n\}$. A graph $G$ is said to admit an inclusive distance antimagic labeling if every pair of distinct vertices has different weights, with a vertex weight is defined by $w(v) = \sum_{u \in N(v)} f(u) + f(v)$. Furthermore, if the vertex weights form an arithmetic progression with the first term $a$ and the common difference $d$, then $G$ is said to admit an $(a,d)$-inclusive distance antimagic labeling. This paper investigates the inclusive distance antimagic labeling of the shadow graph of the complete and circulant graph.