منابع مشابه
On the Unitary Cayley Graph of a Ring
Let R be a ring with identity. The unitary Cayley graph of a ring R, denoted by GR, is the graph, whose vertex set is R, and in which {x, y} is an edge if and only if x − y is a unit of R. In this paper we find chromatic, clique and independence number of GR, where R is a finite ring. Also, we prove that if GR ' GS , then GR/JR ' GS/JS , where JR and JS are Jacobson radicals of R and S, respect...
متن کاملOn the Unitary Cayley Graph of a Finite Ring
We study the unitary Cayley graph associated to an arbitrary finite ring, determining precisely its diameter, girth, eigenvalues, vertex and edge connectivity, and vertex and edge chromatic number. We also compute its automorphism group, settling a question of Klotz and Sander. In addition, we classify all planar graphs and perfect graphs within this class.
متن کاملon spectra of unitary cayley mixed graph
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 $n$.
متن کاملOn the Zero-divisor Cayley Graph of a Finite Commutative Ring
Let R be a fnite commutative ring and N(R) be the set of non unit elements of R. The non unit graph of R, denoted by Gamma(R), is the graph obtained by setting all the elements of N(R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x - yin N(R). In this paper, the basic properties of Gamma(R) are investigated and some characterization results regarding co...
متن کاملColor energy of a unitary Cayley graph
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. [1] have introduced the concept of color energy of a graph Ec(G) and computed the color energy of few families of graphs with χ(G) colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the co...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2214