Planar, Toroidal, and Projective Commuting and Noncommuting Graphs

DOI10.1080/00927872.2014.910796zbMath1327.05145arXiv1402.4978OpenAlexW1515095029WikidataQ58841456 ScholiaQ58841456MaRDI QIDQ5500723

Kazem Khashyarmanesh, Mojgan Afkhami, Mohammad Farrokhi D. G.

Publication date: 7 August 2015

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.4978

zbMATH Keywords

genuscommuting graphnoncommuting graphcrosscap

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (16)

Non-solvable graphs of groups ⋮ Connectivity and planarity of g-noncommuting graph of finite groups ⋮ Unnamed Item ⋮ REALIZABILITY PROBLEM FOR COMMUTING GRAPHS ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Characterization of groups with planar, toroidal or projective planar (proper) reduced power graphs ⋮ Power graphs of (non)orientable genus two ⋮ Various energies of commuting graphs of some super integral groups ⋮ Solvable graphs of finite groups ⋮ Graphs defined on groups ⋮ Unnamed Item ⋮ The complement of proper power graphs of finite groups ⋮ On Laplacian energy of non-commuting graphs of finite groups ⋮ Groups whose non-commuting graph on a transversal is planar or toroidal ⋮ The metric dimension & distance spectrum of non-commuting graph of dihedral group

Uses Software

• GAP

Cites Work

• Orientable and non orientable genus of the complete bipartite graph
• 103 graphs that are irreducible for the projective plane
• Non-commuting graph of a group.
• What is the Probability that Two Group Elements Commute?
• Simple groups are characterized by their non-commuting graphs
• Inequalities involving the genus of a graph and its thicknesses
• Groups Whose Elements are of Order Two or Three

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