Results 1 to 10 of about 103 (99)
Color Energy Of A Unitary Cayley Graph
Discussiones Mathematicae Graph Theory, 2014 Let G be a vertex colored graph. The minimum number χ(G) of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al.
Adiga Chandrashekar +2 more
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Unitary Cayley graphs of Dedekind domain quotients
AKCE International Journal of Graphs and Combinatorics, 2016 If X is a commutative ring with unity, then the unitary Cayley graph of X, denoted GX, is defined to be the graph whose vertex set is X and whose edge set is {{a,b}:a−b∈X×}.
Colin Defant
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On spectra of unitary Cayley mixed graph [PDF]
Transactions on Combinatorics, 2016 In this paper we introduce mixed unitary Cayley graph $M_{n}$ $(n>1)$ and compute its eigenvalues. We also compute the energy of $M_{n}$ for some $n$.
Chandrashekar Adiga +1 more
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Nordhaus-gaddum type inequalities for tree covering numbers on unitary cayley graphs of finite rings [PDF]
Transactions on Combinatorics, 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 disjoint
Denpong Pongpipat, Nuttawoot Nupo
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Graphs Defined on Rings: A Review
Mathematics, 2023 The study on graphs emerging from different algebraic structures such as groups, rings, fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and graph theory are two mathematical fields that focus on creating and ...
S. Madhumitha, Sudev Naduvath
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UNIT AND UNITARY CAYLEY GRAPHS FOR THE RING OF EISENSTEIN INTEGERS MODULO \(n\)
Ural Mathematical Journal, 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, the
Reza Jahani-Nezhad, Ali Bahrami
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Some Properties of Unitary Cayley Graphs [PDF]
The Electronic Journal of Combinatorics, 2007 The unitary Cayley graph $X_n$ has vertex set $Z_n=\{0,1, \ldots ,n-1\}$. Vertices $a, b$ are adjacent, if gcd$(a-b,n)=1$. For $X_n$ the chromatic number, the clique number, the independence number, the diameter and the vertex connectivity are determined. We decide on the perfectness of $X_n$ and show that all nonzero eigenvalues of $X_n$ are integers
Klotz, Walter, Sander, Torsten
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Domination Parameters of the Unitary Cayley Graph of /n
Discussiones Mathematicae Graph Theory, 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.
Burcroff Amanda
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On the Unitary Cayley Signed Graphs [PDF]
The Electronic Journal of Combinatorics, 2011 A $signed graph$ (or $sigraph$ in short) is an ordered pair $S = (S^u, \sigma)$, where $S^u$ is a graph $G = (V, E)$ and $\sigma : E\rightarrow \{+,-\}$ is a function from the edge set $E$ of $S^u$ into the set $\{+, -\}$. For a positive integer $n > 1$, the unitary Cayley graph $X_n$ is the graph whose vertex set is $Z_n$, the integers modulo $n ...
Sinha, Deepa, Garg, Pravin
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On the Energy of Unitary Cayley Graphs [PDF]
The Electronic Journal of Combinatorics, 2009 In this note we obtain the energy of unitary Cayley graph $X_{n}$ which extends a result of R. Balakrishnan for power of a prime and also determine when they are hyperenergetic. We also prove that ${E(X_{n})\over 2(n-1)}\geq{2^{k}\over 4k}$, where $k$ is the number of distinct prime divisors of $n$.
Ramaswamy, H. N., Veena, C. R.
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