the maximum number of edges in a strongly multiplicative graph

The Maximum Number of Edges in a Strongly Multiplicative Graph

An upper bound for maximum number of edges in a strongly multiplicative graph

In this note we give an upper bound for λ(n), the maximum number of edges in a strongly multiplicative graph of order n, which is sharper than the upper bounds given by Beineke and Hegde [3] and Adiga, Ramaswamy and Somashekara [2], for n ≥ 28.

On the Maximum Number of Dominating Classes in Graph Coloring

In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].  

The maximum number of edges in a graph of bounded dimension, with applications to ring theory

With a nite graph G V E we associate a partially ordered set P X P with X V E and x e in P if and only if x is an endpoint of e in G This poset is called the incidence poset of G In this paper we consider the function M p d de ned for p d as the maximum number of edges a graph G can have when it has p vertices and the dimension of its incidence poset is at most d It is easy to see that M p p as...

The number of removable edges in a 4-connected graph

Let G be a 4-connected graph. For an edge e of G; we do the following operations on G: first, delete the edge e from G; resulting the graph G e; second, for all the vertices x of degree 3 in G e; delete x from G e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G~e: If G~e is st...

On the number of cut edges in a regular graph

A cut edge in a graph G is an edge whose removal increases the number of connected components of G. In this paper we determine the maximum number of cut edges in a connected d-regular graph G of order p.