Abstract
Let be a connected graph. For any two vertices and , let denote the distance between and in . The maximum distance between any pair of vertices of is called the diameter of and denoted by . A radio labeling (or multilevel distance labeling) of is a function that assigns to each vertex a label from the set such that the following holds for any vertices and : . The span of is defined as . The radio number of is the minimum span over all radio labelings of . The fourth power of is a graph constructed from by adding edges between vertices of distance four or less apart in . In this paper, we completely determine the radio number for the fourth power of any path, except when its order is congruent to .
Citation
Min-Lin Lo. Linda Victoria Alegria. "Radio number for fourth power paths." Involve 9 (2) 317 - 332, 2016. https://doi.org/10.2140/involve.2016.9.317
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