in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

Let ‘G’ be a graph. If u,v ∈V, then u-v geodetic of G is the shortest path between u and v. The closed interval I[u, v] consists all vertices lying in some G. For S⊆V(G) set I[S] union sets I [u, for u,v∈S. A S if I[S]=V(G). cardinality minimum number G, denoted by g(G). graph split 〈V-S〉 disconnected, g_s (G) In this paper study restrained strong product lexicographic graphs. subgraph disconne...

For two vertices u and v of a connected graph G, the set IG[u, v] consists of all those vertices lying on u − v geodesics in G. Given a set S of vertices of G, the union of all sets IG[u, v] for u, v ∈ S is denoted by IG[S]. A set S ⊆ V (G) is a geodetic set if IG[S] = V (G) and the minimum cardinality of a geodetic set is its geodetic number g(G) of G. Bounds for the geodetic number of strong ...

For a connected graph G with at least two vertices and S a subset of vertices, the convex hull [S]G is the smallest convex set containing S. The hull number h(G) is the minimum cardinality among the subsets S of V (G) with [S]G = V (G). Upper bound for the hull number of strong product G⊠H of two graphs G and H is obtainted. Improved upper bounds are obtained for some class of strong product gr...