March 10, 2024Open Access

Connectivity of 3-distance graphs

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Resumen

For a simple graph G, the 3-distance graph, D₃ (G), is a graph with the vertex set V (G) and two vertices are adjacent if and only if their distance is 3 in the graph G. For a connected graph G, we provide some conditions for the connectedness of D₃ (G). Also, we characterize all trees and unicyclic graphs with connected 3-distance graph.

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Cite This Study

Musawi et al. (Sun,) studied this question.

synapsesocial.com/papers/68e74cd0b6db6435876c535d https://doi.org/https://doi.org/10.48550/arxiv.2403.06132

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1The Structure of Graphs Whose Vertices of Degree at Least Three Are at a Distance of at Least Three2026
2Diameter of 2-distance graphs2024
3Properties of uniformly $3$-connected graphs2024
4Distance Critical Graphs2024
5Bounds on the difference between the eccentric distance sum and the degree distance of graphs2025

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