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Let G = (V, E) be a graph and let k be a positive integer. Let P k (V)={S : S ⊆ V and |S| = k}. The k-token graph F k (G) is the graph with vertex set P k (V) and two vertices A and B are adjacent if A∆B = {a, b} and ab ∈ E(G), where ∆ denotes the symmetric difference. In this paper we present several basic results on 2-token graphs.

In this paper we discuss several operations on fuzzy graphs such as union, join, composition, Cartesian product and study their domination parameters.

Let Z(R) be the set of zero-divisors of a commutative ring R with non-zero identity and Z Ã ðRÞ ¼ ZðRÞ n f0g be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by CðRÞ, is a simple graph whose vertex set is Z Ã ðRÞ and two vertices u, v 2 Z Ã ðRÞ are adjacent if and only if uv ¼ vu ¼ 0: In this paper, we investigate the adjacency matrix and the spectrum of the zerodivisor graphs CðZ n Þ for n ¼ p M q N , where p < q are primes and M, N are positive integers. Moreover, we obtain the clique number, stability number and girth of CðZ p M q N Þ: