p-Graphs Associated with Some Groups and Vice Versa

Abstract

Given a finite group G with a subset where is a prime. The -graphs denoted by whose vertices are the elements of and where two distinct vertices and are adjacent if or . The algebraic structure of such -graphs has been investigated using Java programming language with NetBeans IDE. Then, a method is proposed to convert the graph structure to a group-like form.

Solving Edges Deletion Problem of Generalized Petersen Graphs

“…Suppose the graph 𝐺 = (𝑉, 𝐸) is an undirected and simple graph, where 𝐸(𝐺) denotes the set of edges of size 𝑚 and 𝑉(𝐺) represents the set of vertices of order 𝑛. In graph 𝐺, a Hamiltonian path is a path that passes through each vertex precisely once [7]. A Hamiltonian path in a graph with 𝑛 vertices have 𝑛 − 1 edges, while a Hamiltonian cycle has 𝑛 edges [8].…”

r-Domination Number for Some Special Graphs

“…The open neighborhood of a vertex 𝑤 is the set 𝑁(𝑤) = {𝑢 ∈ 𝑉, 𝑢𝑤 ∈ 𝐸(𝐺) } and closed neighborhood is the set 𝑁[𝑢] = 𝑁(𝑢) ∪ {𝑢}. Graph theory has several topics for more information about it see [1][2][3]. The study of domination problem is grown fast in graph theory.…”