Several properties of antiadjacency matrices of directed graphs

Kiki A. Sugeng, Fery Firmansah, Wildan, Bevina D. Handari, Nora Hariadi, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

Abstract

Let G be a directed graph with order n. The adjacency matrix of the directed graph G is a matrix A = [aij] of order n × n, such that for i ≠ j, if there is an arc from i to j, then aij = 1, otherwise aij = 0. Matrix B = J − A is called the antiadjacency matrix of the directed graph G, where J is the matrix of order n × n with all of those entries are one. In this paper, we provided several properties of the adjacency matrices of directed graphs, such as a determinant of a directed graphs, the characteristic polynomial of acyclic directed graphs, and regular directed graphs. Moreover, we discuss antiadjacency energy of acyclic directed graphs and give some examples of antiadjacency energy for several families of graphs.

Original languageEnglish
Pages (from-to)27834-27847
Number of pages14
JournalAIMS Mathematics
Volume9
Issue number10
DOIs
Publication statusPublished - 2024

Keywords

  • antiadjacency matrix
  • characteristic polynomial
  • directed acyclic graph
  • energy of directed graph
  • spectrum

Fingerprint

Dive into the research topics of 'Several properties of antiadjacency matrices of directed graphs'. Together they form a unique fingerprint.

Cite this