Abstract
The aim of this article is to compute the signless and normalized Laplacian spectrums of the power graph, its main supergraph and cyclic graph of dihedral and dicyclic groups.
Highlights
The aim of this article is to compute the signless and normalized Laplacian spectrums of the power graph, its main supergraph and cyclic graph of dihedral and dicyclic groups
The investigation of graphs related to algebraic structures is important, because graphs like these have important applications and are related to automata theory
Y ∈ G are adjacent in the power graph if and only if one is a power of the other
Summary
The aim of this article is to compute the signless and normalized Laplacian spectrums of the power graph, its main supergraph and cyclic graph of dihedral and dicyclic groups. Cameron and Ghosh in [1], proved that abelian groups with the same number of elements of each possible order can be characterized by their power graphs. In [4, 5], the present author introduced the main supergraph S(G), that is a graph with vertex set G in which two vertices x and y are adjacent if and only if o(x)|o(y) or o(y)|o(x).
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