Unbounded Mixed Resolvability of Web Graph and Prism Related Graph

TL;DR

This paper investigates the mixed metric dimension of Web graphs and Prism allied graphs, revealing that it is unbounded and that their mixed metric basis sets are independent.

Contribution

It computes the mixed metric dimension for Web and Prism allied graphs and shows it is unbounded, also proving the independence of their basis sets.

Findings

Mixed metric dimension is unbounded for both graph families.

Mixed metric basis sets are independent.

Provides explicit computations for these graph families.

Abstract

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.