Co-prime order graphs of finite Abelian groups and dihedral groups Article Swipe

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Dihedral group Combinatorics Mathematics Abelian group p-group Cyclic group Vertex (graph theory) Non-abelian group Finite group Prime (order theory) Discrete mathematics Dihedral angle Graph Elementary abelian group Circulant graph Group (periodic table) Voltage graph Physics Line graph Hydrogen bond Molecule Quantum mechanics

Amit Sehgal , Manjeet Manjeet , Dalip Singh ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.22436/jmcs.023.03.03 · OA: W3012633103

The \\textbf{Co-Prime Order Graph} $\\Theta (G)$ of a given finite group is a\nsimple undirected graph whose vertex set is the group $G$ itself, and any two\nvertexes x,y in $\\Theta (G)$ are adjacent if and only if $gcd(o(x),o(y))=1$ or\nprime. In this paper, we find a precise formula to count the degree of a vertex\nin the Co-Prime Order graph of a finite abelian group or Dihedral group\n$D_n$.We also investigate the Laplacian spectrum of the Co-Prime Order Graph\n$\\Theta (G)$ when G is finite abelian p-group, ${\\mathbb{Z}_p}^t \\times\n{\\mathbb{Z}_q}^s$ or Dihedral group $D_{p^n}$.\n Key Words and Phrases: Co-Prime Order graph,finite abelian group,Dihedral\ngroup, Laplacian spectrum.\n

Co-prime order graphs of finite Abelian groups and dihedral groups Article Swipe

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