Integral Cayley graphs over a group of order 6n

Jing Wang; Xiaogang Liu; Ligong Wang

doi:10.1080/03081087.2025.2480554

Integral Cayley graphs over a group of order 6n

Jing Wang, Xiaogang Liu, Ligong Wang

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

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

Abstract

In this paper, we study the integral Cayley graphs over a non-abelian group (Formula presented.) of order (Formula presented.). We give a necessary and sufficient condition for the integrality of Cayley graphs over (Formula presented.). We also study relationships between the integrality of Cayley graphs over (Formula presented.) and the Boolean algebra of cyclic groups. As applications, we construct some infinite families of connected integral Cayley graphs over (Formula presented.).

Original language	English
Journal	Linear and Multilinear Algebra
DOIs	https://doi.org/10.1080/03081087.2025.2480554
State	Accepted/In press - 2025

Keywords

Boolean algebra
Integral Cayley graph
non-abelian group

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10.1080/03081087.2025.2480554

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title = "Integral Cayley graphs over a group of order 6n",

abstract = "In this paper, we study the integral Cayley graphs over a non-abelian group (Formula presented.) of order (Formula presented.). We give a necessary and sufficient condition for the integrality of Cayley graphs over (Formula presented.). We also study relationships between the integrality of Cayley graphs over (Formula presented.) and the Boolean algebra of cyclic groups. As applications, we construct some infinite families of connected integral Cayley graphs over (Formula presented.).",

keywords = "Boolean algebra, Integral Cayley graph, non-abelian group",

author = "Jing Wang and Xiaogang Liu and Ligong Wang",

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AU - Wang, Jing

AU - Liu, Xiaogang

AU - Wang, Ligong

PY - 2025

Y1 - 2025

N2 - In this paper, we study the integral Cayley graphs over a non-abelian group (Formula presented.) of order (Formula presented.). We give a necessary and sufficient condition for the integrality of Cayley graphs over (Formula presented.). We also study relationships between the integrality of Cayley graphs over (Formula presented.) and the Boolean algebra of cyclic groups. As applications, we construct some infinite families of connected integral Cayley graphs over (Formula presented.).

AB - In this paper, we study the integral Cayley graphs over a non-abelian group (Formula presented.) of order (Formula presented.). We give a necessary and sufficient condition for the integrality of Cayley graphs over (Formula presented.). We also study relationships between the integrality of Cayley graphs over (Formula presented.) and the Boolean algebra of cyclic groups. As applications, we construct some infinite families of connected integral Cayley graphs over (Formula presented.).

KW - Boolean algebra

KW - Integral Cayley graph

KW - non-abelian group

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JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

ER -

Integral Cayley graphs over a group of order 6n

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Keywords

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