The antiadjacency spectrum of some graph operations

Farhan, Mohammad; John, Peter; Silaban, Denny Riama

doi:10.47974/JDMSC-2346

Open Access Research Article

The antiadjacency spectrum of some graph operations

Mohammad Farhanmohammad.farhan81@alumni.ui.ac.idDepartment of MathematicsFaculty of Mathematics and Natural SciencesUniversitas IndonesiaDepok, 16424, Indonesia0009-0000-2381-7919View full profile → , Peter Johnpeter.john@sci.ui.ac.idDepartment of MathematicsFaculty of Mathematics and Natural SciencesUniversitas IndonesiaDepok, 16424, IndonesiaView full profile → , ^*Denny Riama SilabanCorresponding authordenny@sci.ui.ac.idDepartment of MathematicsFaculty of Mathematics and Natural SciencesUniversitas IndonesiaDepok, 16424, Indonesia0000-0003-1721-4438View full profile →

* Corresponding author · click or hover a name for details

pp. 1629–1650Vol. 29Issue 4April 2026DOI: 10.47974/JDMSC-2346 Crossmark XML

Received:: 01 Nov 2024
Published Online:: 28 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2346
Pages:: 1629–1650

Abstract

Let Γ = (V, E) be a graph of order η with V = {1, 2, 3, …, η} and E ⊆ [V]2. The antiadjacency matrix of Γ is an η × η matrix where the ij-entry is 1 if ij ∉ E and 0 if otherwise. An antiadjacency matrix can be seen as the opposite of the adjacency matrix of graphs. In this paper, we give the spectrum of the antiadjacency matrix of some graph operations, namely, disjoint union of circulant graphs, Cartesian product of cycle graph and complete graph of order two, disjoint union of complete graphs, complement of a graph, and join of graphs.

Keywords

Antiadjacency matrix Spectrum Cartesian product Join Disjoint union

Subject Classifications

05C50

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