Direct sum graph of the subspaces of a finite dimensional vector space over finite fields

2023/09/30 by Wani, Bilal A., Altaf, Aaqib, Pirzada, S. +1
#05C25 #05C69 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.00251

Abstract

In this paper, we introduce a new graph structure, called the direct~ sum ~graph on a finite dimensional vector space. We investigate the connectivity, diameter and the completeness of Γ_{U⊕ W}(\mathbbV). Further, we find its domination number and independence number. We also determine the degree of each vertex in case the base field is finite and show that the graph Γ_{U⊕ W}(\mathbbV) is not Eulerian. We also show that under some mild conditions the graph Γ_{U⊕ W}(\mathbbV) is triangulated. We determine the clique number of Γ_{U⊕ W}(\mathbbV) for some particular cases. Finally, we find the size, girth, edge-connectivity and the chromatic number of Γ_{U⊕ W}(\mathbbV).

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