https://doi.org/10.30598/barekengvol16iss2pp497–506 June 2022 Volume 16 Issue 2 Page 497–506 P-ISSN: 1978-7227 E-ISSN: 2615-3017 BAREKENG: Jurnal Ilmu Matematika dan Terapan 497 https://ojs3.unpatti.ac.id/index.php/barekeng/ barekeng.math@yahoo.com ON ANTIADJACENCY MATRIX OF A DIGRAPH WITH DIRECTED DIGON(S) Muhammad Irfan Arsyad Prayitno 1* , Kiki Ariyanti Sugeng 2 1,2 Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Indonesia, 10430, Indonesia Corresponding author’s e-mail: ¹* mirfanaps@sci.ui.ac.id Abstract. The antiadjacency matrix is one representation matrix of a digraph. In this paper, we find the determinant and the characteristic polynomial of the antiadjacency matrix of a digraph with directed digon(s). The digraph that we will discuss is a digraph obtained by adding arc(s) in an arborescence path digraph such that it contained directed digon(s), and a digraph obtained by deleting arc(s) in a complete star digraph. We found that the determinant and the coefficient of the characteristic polynomial of the antiadjacency matrix of a digraph obtained by adding arc(s) in an arborescence path digraph such that it contained directed digon(s) is different depending on the location of the directed digon. Meanwhile, the determinant of the antiadjacency matrix of a digraph obtained by deleting arc(s) in the complete star digraph is zero. Keywords: antiadjacency matrix, arc, characteristic polynomial, determinant, digraph, directed digon. Article info: Submitted: 5 th February 2022 Accepted: 20 th April 2022 How to cite this article: M. I. A. Prayitno and K. A. Sugeng, “ON ANTIADJACENCY MATRIX OF A DIGRAPH WITH DIRECTED DIGON(S)”, BAREKENG: J. Il. Mat. & Ter., vol. 16, iss. 2, pp. 497-506, June, 2022. This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Copyright © 2022 Muhammad Irfan Arsyad Prayitno, Kiki Ariyanti Sugeng