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Degree diameter problem on triangular networks

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posted on 2025-05-08, 17:53 authored by Přemysl Holub, Joseph RyanJoseph Ryan
The degree diameter problem involves finding the largest graph (in terms of number of vertices) subject to constraints on the degree and the diameter of the graph. Beyond the degree constraint there is no restriction on the number of edges (apart from keeping the graph simple) so the resulting graph may be thought of as being embedded in the complete graph. In a generalisation of this problem, the graph is considered to be embedded in some connected host graph. This article considers embedding the graph in the triangular grid and provides some exact values and some upper and lower bounds for the optimal graphs. Moreover, all the optimal graphs are 2-connected, without this constraints no larger graphs were found.

History

Journal title

Australasian Journal of Combinatorics

Volume

63

Issue

3

Pagination

333-345

Publisher

Centre for Discrete Mathematics & Computing, University of Queensland

Place published

Brisbane, QLD

Language

  • en, English

College/Research Centre

Faculty of Engineering and Built Environment

School

School of Electrical Engineering and Computer Science

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