Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two
The paper deals with Hamiltonian and pancyclic graphs in the class of all self-centered graphs of radius 2. For both of the two considered classes of graphs we have done the following. For a given number n of vertices, we have found an upper bound of the minimum size of such graphs. For n ≤ 12 we ha...
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Online Access: | https://doi.org/10.7151/dmgt.2042 |
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doaj-86b14de758e54ace90ed8c3f59d688862021-09-05T17:20:23ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922018-08-0138366168110.7151/dmgt.2042dmgt.2042Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius TwoHrnčiar Pavel0Monoszová Gabriela1Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01Banská Bystrica, SlovakiaDepartment of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01Banská Bystrica, SlovakiaThe paper deals with Hamiltonian and pancyclic graphs in the class of all self-centered graphs of radius 2. For both of the two considered classes of graphs we have done the following. For a given number n of vertices, we have found an upper bound of the minimum size of such graphs. For n ≤ 12 we have found the exact values of the minimum size. On the other hand, the exact value of the maximum size has been found for every n. Moreover, we have shown that such a graph (of order n and) of size m exists for every m between the minimum and the maximum size. For n ≤ 10 we have found all nonisomorphic graphs of the minimum size, and for n = 11 only for Hamiltonian graphs.https://doi.org/10.7151/dmgt.2042self-centered graph with radius 2hamiltonian graphpancyclic graphsize of graph05c1205c3505c45 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hrnčiar Pavel Monoszová Gabriela |
spellingShingle |
Hrnčiar Pavel Monoszová Gabriela Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two Discussiones Mathematicae Graph Theory self-centered graph with radius 2 hamiltonian graph pancyclic graph size of graph 05c12 05c35 05c45 |
author_facet |
Hrnčiar Pavel Monoszová Gabriela |
author_sort |
Hrnčiar Pavel |
title |
Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two |
title_short |
Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two |
title_full |
Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two |
title_fullStr |
Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two |
title_full_unstemmed |
Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two |
title_sort |
hamiltonian and pancyclic graphs in the class of self-centered graphs with radius two |
publisher |
Sciendo |
series |
Discussiones Mathematicae Graph Theory |
issn |
2083-5892 |
publishDate |
2018-08-01 |
description |
The paper deals with Hamiltonian and pancyclic graphs in the class of all self-centered graphs of radius 2. For both of the two considered classes of graphs we have done the following. For a given number n of vertices, we have found an upper bound of the minimum size of such graphs. For n ≤ 12 we have found the exact values of the minimum size. On the other hand, the exact value of the maximum size has been found for every n. Moreover, we have shown that such a graph (of order n and) of size m exists for every m between the minimum and the maximum size. For n ≤ 10 we have found all nonisomorphic graphs of the minimum size, and for n = 11 only for Hamiltonian graphs. |
topic |
self-centered graph with radius 2 hamiltonian graph pancyclic graph size of graph 05c12 05c35 05c45 |
url |
https://doi.org/10.7151/dmgt.2042 |
work_keys_str_mv |
AT hrnciarpavel hamiltonianandpancyclicgraphsintheclassofselfcenteredgraphswithradiustwo AT monoszovagabriela hamiltonianandpancyclicgraphsintheclassofselfcenteredgraphswithradiustwo |
_version_ |
1717786378365829120 |