Fractional local edge dimensions of a graph

Abstract

Metric-based parameters aided the study of the structural properties of graph network space like complexity, central tendency, connectivity, robustness, accessibility, and vulnerability. At the same time, these parameters played a pivotal role in rectifying problems in navigation, integer programming, optimization, pattern recognition and avoidance, combinatoric detection, backtracking in geographical routing, etc. In this paper, we considered the fractional edge dimension, a metric-based parameter in local environment by initiating the study of the fractional local edge dimensions of a graph (FLED). We define the aforesaid concept and give its bounds. We discussed the characterization problem for FLED equal to [Formula: see text], the realization problem, and its relation with the fractional metric dimensions. We also calculated the FLED of the Petersen graph, Coxeter graph, the families of cycle, complete, wheel, grid and complete [Formula: see text]-partite graphs.