A set S ⊆ V (G) of an undirected graph G is a locating-dominating if for each v ∈ \ S, there exists w such tha vw E(G) and NG(x) ∩ ̸= NG(y) any two distinct vertices x y in S. stable it {v} The minimum cardinality G, denoted by γSLD(G), called the locating-domination number G. In this paper, we investigate concept corresponding parameter edge corona lexicographic product graphs.

Let G be a connected graph and k ≥ 1 an integer. The open k-neighborhood Nk G(v) of v ∈ V (G) is the set = {u \ {v}: dG(u, v) ≤ k}. A S vertices called distance k-cost effective if for every vertex u in S, |Nk G(u) ∩ (V S)| − S| 0. maximum cardinality upper number G. In this paper, we characterized sets corona lexicographic product two graphs. Consequently, bounds or exact values numbers these ...

Let G,H be graphs and G?H represent a particular graph product of G H. We define im(G) to the largest t such that has Kt-immersion ask: given im(G)=t im(H)=r, how large is im(G?H)? Best possible lower bounds are provided when ? Cartesian or lexicographic product, conjecture offered for each direct strong products, along with some partial results.

Hahn’s famous structure theorem states that totally ordered Abelian groups can be embedded in the lexicographic product of real groups. Our main theorem extends this structural description to order-dense, commutative, group-like residuated chains, which has only finitely many idempotents. It is achieved via the so-called partial-lexicographic product construction (to be introduced here) using t...

The quadratic embedding constant (QE constant) of a graph is new characteristic value defined through the distance matrix. We derive formulae for QE constants join two regular graphs, double graphs and certain lexicographic product graphs. Examples include complete bipartite wheel friendship completely split graph, some associated to strongly