TY - JOUR

T1 - Properties of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic tadpole graph

AU - Qomaruzzaman,

AU - Aminah, S.

AU - Sugeng, K. A.

N1 - Publisher Copyright:
© 2021 Published under licence by IOP Publishing Ltd.

PY - 2021/3/23

Y1 - 2021/3/23

N2 - A directed cyclic graph is a directed graph that has at least one directed cycle graph, that is a cycle graph in which all edges are oriented, so that the direction passes through each vertex once, except the end of vertex. The directed unicyclic tadpole graph Tm, n is the graph created by concatenating a cycle Cm and a path Pn with an edge from any vertex of Cm to a pendant of Pn for integers m = 3 and n = 1. Antiadjacency matrix is a directed graph representation matrix based on whether or not there is a relation between one vertex and the others. This paper gives the general form of coefficients of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic tadpole graph. To find the general form of coefficients of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic tadpole graph we need to do the grouping of induced subgraphs into acyclic and cyclic and verify with related theorems. After that, the characteristic polynomial is factorized and the roots are calculatedto find its eigenvalues. The coefficients of the characteristic polynomial consist of three distinct values and the eigenvalues are divided into odd case and even case.

AB - A directed cyclic graph is a directed graph that has at least one directed cycle graph, that is a cycle graph in which all edges are oriented, so that the direction passes through each vertex once, except the end of vertex. The directed unicyclic tadpole graph Tm, n is the graph created by concatenating a cycle Cm and a path Pn with an edge from any vertex of Cm to a pendant of Pn for integers m = 3 and n = 1. Antiadjacency matrix is a directed graph representation matrix based on whether or not there is a relation between one vertex and the others. This paper gives the general form of coefficients of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic tadpole graph. To find the general form of coefficients of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic tadpole graph we need to do the grouping of induced subgraphs into acyclic and cyclic and verify with related theorems. After that, the characteristic polynomial is factorized and the roots are calculatedto find its eigenvalues. The coefficients of the characteristic polynomial consist of three distinct values and the eigenvalues are divided into odd case and even case.

UR - http://www.scopus.com/inward/record.url?scp=85103547989&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1836/1/012002

DO - 10.1088/1742-6596/1836/1/012002

M3 - Conference article

AN - SCOPUS:85103547989

VL - 1836

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012002

T2 - 4th International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2020

Y2 - 22 August 2020 through 23 August 2020

ER -