What question did this study set out to answer?

This study aims to characterize the structure of connected graphs where certain distance conditions apply to degree-three vertices.

February 14, 2026MathematicsOpen Access

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

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This study aims to characterize the structure of connected graphs where certain distance conditions apply to degree-three vertices.
Defined a connected graph G with specific degree and distance constraints.
Analyzed the relationships and configurations of vertices within G.
Provided structural decomposition of graph G into a tree and a matching.
Established that graph G can be decomposed into distinct structural components.
Identified that G consists of a tree and a matching arrangement.

Implication

This research reveals the structure of graphs with vertices of degree at least three and a specific distance property.

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.

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Cite This Study

Ghazal et al. (2026) studied this question.

synapsesocial.com/papers/699011602ccff479cfe5806e https://doi.org/10.3390/math14040637

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Implication

This research reveals the structure of graphs with vertices of degree at least three and a specific distance property.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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