二面体群的交图

EIGEN MATHEMATICS JOURNAL Pub Date : 2021-12-30 DOI:10.29303/emj.v4i2.119

N. Nurhabibah, A. G. Syarifudin, I. G. A. W. Wardhana, Q. Aini

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引用次数: 2

摘要

有限群G的相交图是一个图(V,E)，其中V是G的所有非平凡子群的集合，E是两个不同子群H＿i, H＿j相邻的边的集合，当且仅当H＿i \cap H＿j \neq E{。本文讨论了二面体群}D＿2n{的交点图，特别是子图、顶点度、半径、直径、周长和支配数。通过研究，我们得到了当n=p^2时，}D＿2n{的相交图包含完全子图}K＿p+2{和}\gamma (\Gamma ＿D＿2n{)=p。{}}

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The Intersection Graph of a Dihedral Group

The intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j are said to be adjacent if and only if H_i \cap H_j \neq {e} . This study discusses the intersection graph of a dihedral group D_{2n} specifically the subgraph, degree of vertices, radius, diameter, girth, and domination number. From this study, we obtained that if n=p^2 then the intersection graph of D_{2n} is containing complete subgraph K_{p+2} and \gamma(\Gamma_{D_{2n}})=p.

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EIGEN MATHEMATICS JOURNAL

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