TY - JOUR

T1 - Eigenvalues of Antiadjacency Matrix of Directed Cyclic Dumbbell Graph

AU - Budiyanto, S.

AU - Utama, S.

AU - Aminah, S.

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

PY - 2018/12/4

Y1 - 2018/12/4

N2 - This paper explains the steps used to find the characteristic polynomial of the antiadjacency matrix of a cyclic dumbbell graph. The antiadjacency matrix of a graph is a matrix whose entries represent whether there is an edge that connects two vertices or not. The general form of the characteristic polynomial includes its eigenvalues. The antiadjacency matrix is obtained by using some theorems, the number of solutions of integer equations, quadratic formula, and polynomials factorization. Finally, results showed that the coefficients of the characteristic polynomial and its eigenvalues were dependent on the number of vertices of the cyclic dumbbell graph.

AB - This paper explains the steps used to find the characteristic polynomial of the antiadjacency matrix of a cyclic dumbbell graph. The antiadjacency matrix of a graph is a matrix whose entries represent whether there is an edge that connects two vertices or not. The general form of the characteristic polynomial includes its eigenvalues. The antiadjacency matrix is obtained by using some theorems, the number of solutions of integer equations, quadratic formula, and polynomials factorization. Finally, results showed that the coefficients of the characteristic polynomial and its eigenvalues were dependent on the number of vertices of the cyclic dumbbell graph.

UR - http://www.scopus.com/inward/record.url?scp=85058274155&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1108/1/012015

DO - 10.1088/1742-6596/1108/1/012015

M3 - Conference article

AN - SCOPUS:85058274155

SN - 1742-6588

VL - 1108

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012015

T2 - 2nd Mathematics, Informatics, Science and Education International Conference, MISEIC 2018

Y2 - 21 July 2018

ER -