Subspace Sum Graph of a Vector Space

2017/02/27 by Angsuman Das, Das, Angsuman
Computer Science · Mathematics · #05C25 #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1702.08245

openalex publication_date 2017/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce a graph structure, called subspace sum graph G(\mathbbV) on a finite dimensional vector space \mathbbV where the vertex set is the collection of non-trivial proper subspaces of a vector space and two vertices W₁,W₂ are adjacent if W₁ + W₂=\mathbbV. The diameter, girth, connectivity, maximal independent sets, different variants of domination number, clique number and chromatic number of G(\mathbbV) are studied. It is shown that two subspace sum graphs are isomorphic if and only if the base vector spaces are isomorphic. Finally some properties of subspace sum graph are studied when the base field is finite.

Citations

• Results on the intersection graphs of subspaces of a vector space
• The Zero-Divisor Graph of a Commutative Ring

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