Several properties of antiadjacency matrices of directed graphs

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

doi:10.3934/math.20241351

Several properties of antiadjacency matrices of directed graphs

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let G be a directed graph with order n. The adjacency matrix of the directed graph G is a matrix A = [a_ij] of order n × n, such that for i ≠ j, if there is an arc from i to j, then a_ij = 1, otherwise a_ij = 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 language	English
Pages (from-to)	27834-27847
Number of pages	14
Journal	AIMS Mathematics
Volume	9
Issue number	10
DOIs	https://doi.org/10.3934/math.20241351
Publication status	Published - 2024

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Keywords

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

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10.3934/math.20241351

Cite this

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title = "Several properties of antiadjacency matrices of directed graphs",

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 {\texttimes} 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 {\texttimes} 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.",

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author = "Sugeng, \{Kiki A.\} and Fery Firmansah and Wildan and Handari, \{Bevina D.\} and Nora Hariadi and Muhammad Imran",

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doi = "10.3934/math.20241351",

language = "English",

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TY - JOUR

T1 - Several properties of antiadjacency matrices of directed graphs

AU - Sugeng, Kiki A.

AU - Firmansah, Fery

AU - Wildan,

AU - Handari, Bevina D.

AU - Hariadi, Nora

AU - Imran, Muhammad

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - antiadjacency matrix

KW - characteristic polynomial

KW - directed acyclic graph

KW - energy of directed graph

KW - spectrum

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U2 - 10.3934/math.20241351

DO - 10.3934/math.20241351

M3 - Article

AN - SCOPUS:85205957026

SN - 2473-6988

VL - 9

SP - 27834

EP - 27847

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 10

ER -

Several properties of antiadjacency matrices of directed graphs

Abstract

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Keywords

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