On the genus of non-zero component union graphs of vector spaces
On the genus of non-zero component union graphs of vector spaces
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 $v\in\mathbb{V}\setminus\{0\},$ the skeleton of $v$ with respect to the basis $\mathbb{B}$ is defined as $S_\mathfrak{B}(v)=\{\alpha_i : v=\sum_{i=1}^{n} a_i\alpha_i, a_i\neq 0\}.$ The non-zero component union graph $\Gamma(\mathbb{V}_\mathfrak{B})$ of $\mathbb{V}$ with respect to …