Subspace Inclusion Graph of a Vector Space
Subspace Inclusion Graph of a Vector Space
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DOI：
10.1080/00927872.2015.1110588
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发表时间：
2016-06
影响因子：
0.7
通讯作者：
Angsuman Das
中科院分区：
文献类型：
--
作者：
Angsuman Das
本文在有限维向量空间𝕍上引入了一种图结构，称为子空间包含图（𝕍），其中顶点集是向量空间的非平凡固有子空间的集合，如果一个顶点包含在另一个顶点中，则两个顶点相邻。研究了k n（𝕍）的直径、周长、团数和色数。证明了两个子空间包含图同构当且仅当基向量空间同构。最后，研究了基域有限时子空间包含图的一些性质。
In this paper, the authors introduce a graph structure, called subspace inclusion graph ℐn(𝕍) on a finite dimensional vector space 𝕍 where the vertex set is the collection of nontrivial proper subspaces of a vector space and two vertices are adjacent if one is contained in other. The diameter, girth, clique number, and chromatic number of ℐn(𝕍) are studied. It is shown that two subspace inclusion graphs are isomorphic if and only if the base vector spaces are isomorphic. Finally, some properties of subspace inclusion graph are studied when the base field is finite.