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- W3204343395 abstract "Let $mathbb{V}$ be an $n$-dimensional vector space over the field $mathbb{F}$ with a basis $mathfrak{B}={alpha_1,ldots,alpha_n}.$ For a non-zero vector $vinmathbb{V}setminus{0},$ the skeleton of $v$ with respect to the basis $mathbb{B}$ is defined as $S_mathfrak{B}(v)={alpha_i : v=sum_{i=1}^{n} a_ialpha_i, a_ineq 0}.$ The non-zero component union graph $Gamma(mathbb{V}_mathfrak{B})$ of $mathbb{V}$ with respect to $mathfrak{B}$ is the simple graph with vertex set $V=mathbb{V}setminus{0}$ and two distinct non-zero vectors $u,v in V$ are adjacent if and only if $S_mathfrak{B}(u)cup S_mathfrak{B}(v)=mathfrak{B}.$ First, we obtain some graph theoretical properties of $Gamma(mathbb{V}_mathfrak{B}).$ Further, we characterize all finite dimensional vector spaces $mathbb{V}$ for which $Gamma(mathbb{V}_mathfrak{B})$ has genus either 0 or 1 or 2. In the last part of the paper, we characterize all finite dimensional vector spaces $mathbb{V}$ for which the cross cap of $Gamma(mathbb{V}_mathfrak{B})$ is 1." @default.
- W3204343395 created "2021-10-11" @default.
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- W3204343395 date "2021-12-14" @default.
- W3204343395 modified "2023-09-24" @default.
- W3204343395 title "On the genus of non-zero component union graphs of vector spaces" @default.
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- W3204343395 doi "https://doi.org/10.15672/hujms.754535" @default.
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