منابع مشابه
Color 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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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 Energy of Unitary Cayley Graphs
In this note we obtain the energy of unitary Cayley graph Xn which extends a result of R. Balakrishnan for power of a prime and also determine when they are hyperenergetic. We also prove that E(Xn) 2(n−1) ≥ 2 4k , where k is the number of distinct prime divisors of n. Thus the ratio E(Xn) 2(n−1) , measuring the degree of hyperenergeticity of Xn, grows exponentially with k.
متن کاملOn 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.
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2014
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1767