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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, the edge metric dimension and the metric dimension. In this article, we compute the mixed metric dimension for the two families of the plane graphs viz., the Web graph $mathbb{W}_{n}$ and the Prism allied graph $mathbb{D}_{n}^{t}$. We show that the mixed metric dimension is non-constant unbounded for these two families of the plane graph. Moreover, for the Web graph $mathbb{W}_{n}$ and the Prism allied graph $mathbb{D}_{n}^{t}$, we unveil that the mixed metric basis set $M_{G}^{m}$ is independent.
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.
Given a simple graph $G=(V_G, E_G)$ with vertex set $V_G$ and edge set $E_G$, the mixed graph $widetilde{G}$ is obtained from $G$ by orienting some of its edges. Let $H(widetilde{G})$ denote the Hermitian adjacency matrix of $widetilde{G}$ and $A(G)$
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions and the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a certain star de
In 2009, Brown gave a set of conditions which when satisfied imply that a Feynman integral evaluates to a multiple zeta value. One of these conditions is called reducibility, which loosely says there is an order of integration for the Feynman integra
A mixed graph $widetilde{G}$ is obtained by orienting some edges of $G$, where $G$ is the underlying graph of $widetilde{G}$. The positive inertia index, denoted by $p^{+}(G)$, and the negative inertia index, denoted by $n^{-}(G)$, of a mixed graph $