Let X be either Z or the points of a Poisson process in R of intensity 1. Given parameters r and p, join each pair of points of X within distance r independently with probability p. This is the simplest case of a ‘spreadout’ percolation model studied by Penrose [6], who showed that, as r → ∞, the average degree of the corresponding random graph at the percolation threshold tends to 1, i.e., the...

In11, Kulli and Janakiram initiate the concept of maximal domination in graphs. In this paper, we obtained some bounds characterizations. Also, estimate value number graph products such as join graphs, corona product, cartesian product strong product.

Let G be a graph with its vertices and edges. On defining bijective function ρ:V(G) →{0,1,...,p}. For each edge assign the label 1 if ρ*(ab)= | ρ(a) 2 −ρ(b) /ρ(a)−ρ(b) is odd or 0 otherwise such that |eρ(1) − eρ(0)| ≤ then labeling called as divided square difference cordial graph. We prove in this paper for relatively possible set of spider graphs atmost one legs greater than namely J(SP(1 m ,...

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

Given a graph G with weighted edges, and a subset of nodes T, the T-join problem asks for a minimum weight edge set A such that a node u is incident to an odd number of edges of A ii u 2 T. We describe the applications of the T-join problem in sparse graphs to the phase assignment problem in VLSI mask layout and to conformal reenement of nite element meshes. We suggest a practical algorithm for...

Let G be a graph. The first Zagreb polynomial M1(G, x) and the third Zagreb polynomial M3(G, x) of the graph G are defined as:     ( ) ( , ) [ ] e uv E G G x x d(u) + d(v) M1 , ( , )  euvE(G) G x x|d(u) - d(v)| M3 . In this paper, we compute the first and third Zagreb polynomials of Cartesian product of two graphs and a type of dendrimers.