Eigenvalues of antiadjacency matrix of Cayley graph of Z_n

Juan Daniel; Kiki Ariyanti Sugeng; Nora Hariadi

doi:10.19184/ijc.2022.6.1.5

Eigenvalues of antiadjacency matrix of Cayley graph of Z_n

Juan Daniel, Kiki Ariyanti Sugeng, Nora Hariadi

Department of Mathematics

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

Abstract

In this paper, we give a relation between the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) and the eigenvalues of the antiadjacency matrix of Cay(Z_n, (Z_n−{0})−S), as well as the eigenvalues of the adjacency matrix of Cay(Z_n, S). Then, we give the characterization of connection set S where the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) are all integers.

Original language	English
Pages (from-to)	66-76
Journal	Indonesian Journal of Combinatorics
Volume	6
Issue number	1
DOIs	https://doi.org/10.19184/ijc.2022.6.1.5
Publication status	Published - 2022

Keywords

Antiadjacency matrix
Cayley graph
group Zn
eigenvalues
adjacency matrix
circulant matrix

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10.19184/ijc.2022.6.1.5

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abstract = "In this paper, we give a relation between the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) and the eigenvalues of the antiadjacency matrix of Cay(Z_n, (Z_n−{0})−S), as well as the eigenvalues of the adjacency matrix of Cay(Z_n, S). Then, we give the characterization of connection set S where the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) are all integers.",

keywords = "Antiadjacency matrix, Cayley graph, group Zn, eigenvalues, adjacency matrix, circulant matrix",

author = "Juan Daniel and Sugeng, {Kiki Ariyanti} and Nora Hariadi",

year = "2022",

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language = "English",

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journal = "Indonesian Journal of Combinatorics",

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T1 - Eigenvalues of antiadjacency matrix of Cayley graph of Z_n

AU - Daniel, Juan

AU - Sugeng, Kiki Ariyanti

AU - Hariadi, Nora

PY - 2022

Y1 - 2022

N2 - In this paper, we give a relation between the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) and the eigenvalues of the antiadjacency matrix of Cay(Z_n, (Z_n−{0})−S), as well as the eigenvalues of the adjacency matrix of Cay(Z_n, S). Then, we give the characterization of connection set S where the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) are all integers.

AB - In this paper, we give a relation between the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) and the eigenvalues of the antiadjacency matrix of Cay(Z_n, (Z_n−{0})−S), as well as the eigenvalues of the adjacency matrix of Cay(Z_n, S). Then, we give the characterization of connection set S where the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) are all integers.

KW - Antiadjacency matrix

KW - Cayley graph

KW - group Zn

KW - eigenvalues

KW - adjacency matrix

KW - circulant matrix

UR - http://ijc.or.id/index.php/ijc/article/view/162

U2 - 10.19184/ijc.2022.6.1.5

DO - 10.19184/ijc.2022.6.1.5

M3 - Article

SN - 2541-2205

VL - 6

SP - 66

EP - 76

JO - Indonesian Journal of Combinatorics

JF - Indonesian Journal of Combinatorics

IS - 1

ER -

Eigenvalues of antiadjacency matrix of Cayley graph of Z_n

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Keywords

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