Výsledky vyhledávání - "unitary Cayley graph"

Akademický článek

Domination Parameters of the Unitary Cayley Graph of 𝕑/n𝕑

Autor: Burcroff Amanda

Publikováno v: Discussiones Mathematicae Graph Theory, Vol 43, Iss 1, Pp 95-114 (2023)

The unitary Cayley graph of 𝕑/n𝕑, denoted Xn, is the graph with vertex set {0, . . ., n − 1} where vertices a and b are adjacent if and only if gcd(a − b, n) = 1. We answer a question of Defant and Iyer by constructing a family of infinitel

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Akademický článek

Wiener index of graphs over rings: a survey

Autor: T. Asir, V. Rabikka, A. M. Anto, N. Shunmugapriya

Publikováno v: AKCE International Journal of Graphs and Combinatorics, Vol 19, Iss 3, Pp 316-324 (2022)

AbstractThis article presents a survey of results consisting of the Wiener index of graphs associated with commutative rings. In particular, we focus on zero-divisor graphs, unit graphs, total graphs and prime graphs. Further, we have posed some open

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Akademický článek

Nordhaus-gaddum type inequalities for tree covering numbers on unitary cayley graphs of finite rings

Autor: Denpong Pongpipat, Nuttawoot Nupo

Publikováno v: Transactions on Combinatorics, Vol 11, Iss 2, Pp 111-122 (2022)

The unitary Cayley graph $\Gamma_n$ of a finite ring $\mathbb{Z}_n$ is the graph with vertex set $\mathbb{Z}_n$ and two vertices $x$ and $y$ are adjacent if and only if $x-y$ is a unit in $\mathbb{Z}_n$‎. ‎A family $\mathcal{F}$ of mutually edge

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Akademický článek

On Laplacian spectrum of unitary Cayley graphs

Autor: Pirzada S., Barati Z., Afkhami M.

Publikováno v: Acta Universitatis Sapientiae: Informatica, Vol 13, Iss 2, Pp 251-264 (2021)

Let R be a commutative ring with unity 1 ≠ 0 and let R× be the set of all unit elements of R. The unitary Cayley graph of R, denoted by GR = Cay(R, R×), is a simple graph whose vertex set is R and there is an edge between two distinct vertices x

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Akademický článek

UNIT AND UNITARY CAYLEY GRAPHS FOR THE RING OF EISENSTEIN INTEGERS MODULO $n$

Autor: Reza Jahani-Nezhad, Ali Bahrami

Publikováno v: Ural Mathematical Journal, Vol 7, Iss 2 (2021)

Let ${E}_{n}$ be the ring of Eisenstein integers modulo $n$. We denote by $G({E}_{n})$ and $G_{{E}_{n}}$, the unit graph and the unitary Cayley graph of ${E}_{n}$, respectively. In this paper, we obtain the value of the diameter, the girth,

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Akademický článek

Domination in Cayley graphs: A survey

Autor: T. Tamizh Chelvam, M. Sivagami

Publikováno v: AKCE International Journal of Graphs and Combinatorics, Vol 16, Iss 1, Pp 27-40 (2019)

Let be a symmetric generating set of a finite group . Assume that be such that and satisfies the two conditions : the identity element and : if , then Given satisfying and define a Cayley graph with and . When , it is called as circulant graph and de

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