Generalized power graph of groups

2018/07/01 by Abbas Jafarzadeh, Jafarzadeh, Abbas, Peyman Niroomand +3
Computer Science · Engineering · Mathematics · #20D15 #20E34 and 20F18 #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1807.00289

openalex publication_date 2018/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The power graph of an arbitrary group G is a simple graph with all elements of G as its vertices and two vertices are adjacent if one is a positive power of another. In this paper, we generalize this concept to a graph whose vertices are all elements of G that generate a proper subgroup of G and two elements are adjacent if the cyclic subgroup generated by which have non-trivial intersections. We concentrate on completeness and planarity of this graph.

Citations

• Coloring of commutative rings
• On some problems of a statistical group-theory. IV

Related

• Embeddings of (proper) power graphs of finite groups
• Enhanced power graph from the power graph of a group
• Power Graphs of Finite Group
• On the power graph of a finite group
• Some results in a new power graphs in finite groups