Radio numbers for generalized prism graphs

Martinez, Paul; Ortíz, Juan Carlos; Tomova, Maggy; Wyels, Cindy

doi:10.48550/arxiv.1007.5346

Cited by 1 publication

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“…In addition, a previous study determined the radio number for paths and cycles of [25], while the study of the square was performed in the context of paths of [24], and the study of the square was treated in the context of a cycle of [28]. The research conducted in [29] focused on the study results of the radio number for the generalized prism graph. Moreover, in [30] the properties of the generalized gear graph were discussed and the lower bound of its radio number was established.…”

Section: Related Workmentioning

confidence: 99%

Radio Labeling of Supersub—Division of Path Graphs

Mari,

Jeyaraj

2023

IEEE Access

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Motivated by the channel assignment problem, we study the radio labeling of graphs. The radio labeling problem is an important topic in discrete mathematics due to its diverse applications, e.g., frequency assignment in mobile communication systems, signal processing, circuit and sensor network design, etc. A graph labeling problem is an assignment of labels to the vertices or edges (or both) of a graph G that satisfy a mathematical constraint. Radio labeling, a vertex labeling of graphs with non-negative integers, finds an important application in the study of radio channel assignment problems. The maximum label used in a radio labeling is called its span, and the smallest possible span of a radio labeling is called the radio number of a graph. In this area, Liu and Zhu [1] provided important results by computing the exact values of rn(G) for paths and cycles when k is equal to the diameter for certain cases. In this paper, we determine the radio number rn(G) of G where G is the supersub−division of a path P n with n ≥ 3 vertices and a complete bipartite graph K 2,α with α ∈ N.

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Section: Related Workmentioning

confidence: 99%