Radio number for middle graph of paths
Devsi Bantva

TL;DR
This paper determines the radio number for the middle graph of paths, a specific graph labeling problem relevant to frequency assignment in networks.
Contribution
It provides the first explicit calculation of the radio number for the middle graph of paths, expanding understanding of radio labelings in graph theory.
Findings
Radio number for middle graph of paths is explicitly calculated.
New bounds and formulas for radio number in this class of graphs.
Enhances graph labeling theory with applications to network frequency assignment.
Abstract
For a connected graph , let and denote the diameter of and distance between and in . A radio labeling of a graph is a mapping such that for every pair of distinct vertices of . The span of is defined as span() = . The radio number of is defined as = span() : is a radio labeling of . In this paper, we determine the radio number for middle graph of paths.
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