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Volume 14
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Article

The Structure of Graphs Whose Vertices of Degree at Least Three Are at a Distance of at Least Three

by
Salman Ghazal
* and
Steve Karam
College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(4), 637; https://doi.org/10.3390/math14040637
Submission received: 15 January 2026 / Revised: 6 February 2026 / Accepted: 10 February 2026 / Published: 11 February 2026
(This article belongs to the Special Issue Graph Theory and Applications, 3rd Edition)
Versions Notes

Abstract

Let G be a connected graph in which the distance between any two distinct vertices of degree of at least three is at least three. We find the structure of G. It turns out that G decomposes into a tree and a matching.
Keywords: degree; distance; tree; matching degree; distance; tree; matching

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MDPI and ACS Style

Ghazal, S.; Karam, S. The Structure of Graphs Whose Vertices of Degree at Least Three Are at a Distance of at Least Three. Mathematics 2026, 14, 637. https://doi.org/10.3390/math14040637

AMA Style

Ghazal S, Karam S. The Structure of Graphs Whose Vertices of Degree at Least Three Are at a Distance of at Least Three. Mathematics. 2026; 14(4):637. https://doi.org/10.3390/math14040637

Chicago/Turabian Style

Ghazal, Salman, and Steve Karam. 2026. "The Structure of Graphs Whose Vertices of Degree at Least Three Are at a Distance of at Least Three" Mathematics 14, no. 4: 637. https://doi.org/10.3390/math14040637

APA Style

Ghazal, S., & Karam, S. (2026). The Structure of Graphs Whose Vertices of Degree at Least Three Are at a Distance of at Least Three. Mathematics, 14(4), 637. https://doi.org/10.3390/math14040637

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