Cayley subspace sum graph of vector spaces

Authors : G KALAIMURUGAN, S GOPINATH, T TAMIZH CHELVAM

Pages : 1-17

Doi:10.24330/ieja.1195466

View : 13 | Download : 10

Publication Date : 2023-01-09

Article Type : Research Paper

Abstract :Let $\\mathbb{V}$ be a finite dimensional vector space over the field $\\mathbb{F}$. Let $Sinsert ignore into journalissuearticles values(\\mathbb{V});$ be the set of all subspaces of $\\mathbb{V}$ and $\\mathbb{A}\\subseteq S^*insert ignore into journalissuearticles values(\\mathbb{V});=Sinsert ignore into journalissuearticles values(\\mathbb{V});\\backslash\\{0\\}.$ In this paper, we define the Cayley subspace sum graph of $\\mathbb{V},$ denoted by Cay$insert ignore into journalissuearticles values(S^*insert ignore into journalissuearticles values(\\mathbb{V});,\\mathbb{A});, $ as the simple undirected graph with vertex set $S^*insert ignore into journalissuearticles values(\\mathbb{V});$ and two distinct vertices $X$ and $Y$ are adjacent if $X+Z=Y$ or $Y+Z=X$ for some $Z\\in \\mathbb{A}$. Having defined the Cayley subspace sum graph, we study about the connectedness, diameter and girth of several classes of Cayley subspace sum graphs Cay$insert ignore into journalissuearticles values(S^*insert ignore into journalissuearticles values(\\mathbb{V});, \\mathbb{A});$ for a finite dimensional vector space $\\mathbb{V}$ and $\\mathbb{A}\\subseteq S^*insert ignore into journalissuearticles values(\\mathbb{V});=Sinsert ignore into journalissuearticles values(\\mathbb{V});\\backslash\\{0\\}.$
Keywords : Cayley sum graph, vector space, subspace, diameter, girth, planar