Work

Graphs of diameter three are recognizable

Year: 2026

Type: article

Abstract: A vertex-deleted subgraph (or card ) G − v of a graph G is the unlabelled subgraph obtained from G by deleting the vertex v and all edges incident with v . The collection of all cards of G is the deck of G . A graph H is a reconstruction of G if H has the same deck as G . A graph is said to be reconstructible if it is isomorphic to all its reconstructions. A family F of graphs is recognizable if, for each G ∈ F , every reconstruction of G is also in F . In this paper, it is shown that the family of all graphs of diameter three is recognizable.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2026.09.013

Authors: J. Antony Aravind, S. Monikandan

Institution: Manonmaniam Sundaranar University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Department of Atomic Energy, Government of India, National Board for Higher Mathematics