Many large graphs can be constructed from existing smaller graphs by using graph operations, for example, the Cartesian product and the lexicographic product. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this short note, we give some properties of the lexicographic products of vertextransitive and of edge-transitive graphs. In particula...

In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.

Lexicographic product G◦H of two graphs G and H has vertex set V (G)×V (H) and two vertices (u1, v1) and (u2, v2) are adjacent whenever u1u2 ∈ E(G), or u1 = u2 and v1v2 ∈ E(H). If every matching of G of size k can be extended to a perfect matching in G, then G is called k-extendable. In this paper, we study matching extendability in lexicographic product of graphs. The main result is that the l...

Food manufacturers need to understand the taste preferences of their consumers in order to develop successful new products. The existence of consumer segments that differ in systematic ways in their taste preferences can have important implications for product development. Rather than developing a product to please all potential consumers, the manufacturer may decide to optimize the product for...

A linear ordering is said to be representable if it can be order-embedded into the reals. Representable linear orderings have been characterized as those which are separable in the order topology and have at most countably many jumps. We use this characterization to study the representability of a lexicographic product of linear orderings. First we count the jumps in a lexicographic product in ...

We study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesX_{i}. We introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by X boxtimesY. We investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...

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...