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The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an intersection graph.
In this paper, we investigate the problem of covering the vertices of a graph associated to a finite vector space as introduced by Das cite{Das}, such that we can uniquely identify any vertex by examining the vertices that cover it. We use locating-d
Let $mathbb{E}(H)$ and $mathbb{V}(H)$ denote the edge set and the vertex set of the simple connected graph $H$, respectively. The mixed metric dimension of the graph $H$ is the graph invariant, which is the mixture of two important graph parameters,
Write $mathcal{C}(G)$ for the cycle space of a graph $G$, $mathcal{C}_kappa(G)$ for the subspace of $mathcal{C}(G)$ spanned by the copies of the $kappa$-cycle $C_kappa$ in $G$, $mathcal{T}_kappa$ for the class of graphs satisfying $mathcal{C}_kappa(G
We study perfect state transfer in Grover walks, which are typical discrete-time quantum walk models. In particular, we focus on states associated to vertices of a graph. We call such states vertex type states. Perfect state transfer between vertex t
For a graph whose vertex set is a finite set of points in $mathbb R^d$, consider the closed (open) balls with diameters induced by its edges. The graph is called a (an open) Tverberg graph if these closed (open) balls intersect. Using the idea of hal