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Journal : Jurnal Matematika UNAND

On Characteristic Polynomial of Antiadjacency Matrix of A Line Digraph Muhammad Irfan Arsyad Prayitno; Kiki Ariyanti Sugeng
Jurnal Matematika UNAND Vol 11, No 1 (2022)
Publisher : Jurusan Matematika FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmu.11.1.74-81.2022

Abstract

In this paper, we find the characteristic polynomial of the antiadjacency matrix of a line digraph. There are recent studies on the relation between the characteristic polynomial of the adjacency matrix and its line digraph, we are also interested in finding the connection between the antiadjacency matrix of a digraph and its line digraph. In this paper, we show the connection of characteristic polynomial of the antiadjacency matrix between an acyclic digraph and its line digraph.
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)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.1.57-62.2026

Abstract

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.