This article is cited in 2 papers

Scientific Part
Computer Sciences

The construction of all nonisomorphic minimum vertex extensions of the graph by the method of canonical representatives

M. B. Abrosimov^a, I. V. Los'^a, S. V. Kostin<sup>b

a</sup> Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russ
^b MIREA – Russian Technological University, 78 Vernadskogo Ave., Moscow 119454, Russia

Abstract: A graph $G = (V, \alpha)$ is called primitive if there exists a natural $k$ such that between any pair of vertices of the graph $G$ there is a route of length $k$. This paper considers undirected graphs with exponent 2. A criterion for the primitivity of a graph with the exponent 2 and a necessary condition are proved. A graph is primitive with the exponent 2 if and only if its diameter is 1 or 2, and each of its edges is included in a triangle. A computational experiment on the construction of all primitive homogeneous graphs with the number of vertices up to 16 and the exponent 2 is described, its results are analyzed. All homogeneous graphs of orders 2, 3, and 4, which are primitive with the exponent 2, are given, and for homogeneous graphs of order 5, the number of primitive graphs with the exponent 2 is determined.

Key words: primitive graphs, exponent of graph, regular graphs.

UDC: 519.17

Received: 24.07.2020
Revised: 12.10.2020

DOI: 10.18500/1816-9791-2021-21-2-238-245

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