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
N1 - Publisher Copyright:
© 2024 the Author(s), licensee AIMS Press.
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
UR - http://www.scopus.com/inward/record.url?scp=85205957026&partnerID=8YFLogxK
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 -