Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

A graph   is called integral if all eigenvalues of its adjacency matrix  are integers.  Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$.  In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.

in a graph g = (v,e), a subset s  v is said to be an open packing set if no two vertices of s have a common neighbour in g. the maximum cardinality of an open packing set is called the open packing number and is denoted by rho^o. this paper further studies on this parameter by obtaining some new bounds.

We prove that for every k there is a k -chromatic graph with a k-coloring where the neighbors of each color-class form an independent set. This answers a question raised by N. J. A. Harvey and U. S. R. Murty [4]. In fact we find the smallest graph Gk with the required property for

For every positive integer k, a set S of vertices in a graph G = (V;E) is a k- tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum cardinality of a k-tuple dominating set of G is the k-tuple domination number of G. When k = 1, a k-tuple domination number is the well-studied domination...