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

ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH

Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain var...

The Maximum Number of Edges in a Strongly Multiplicative Graph

A note on a graph related to the comaximal ideal graph of a commutative ring

  ‎The rings considered in this article are commutative with identity which admit at least two maximal ideals‎.  ‎This article is inspired by the work done on the comaximal ideal graph of a commutative ring‎. ‎Let R be a ring‎.  ‎We associate an undirected graph to R denoted by mathcal{G}(R)‎,  ‎whose vertex set is the set of all proper ideals I of R such that Inotsubseteq J(R)‎, ‎where J(R) is...

Calculating Different Topological Indices of Von Neumann Regular Graph of Z_(p^α )

By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...

Adjacency metric dimension of the 2-absorbing ideals graph

Let Γ=(V,E) be a graph and ‎W_(‎a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),‎…‎ ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...