The chromaticity of the join of tree and null graph
The chromaticity of the graph G, which is join of the tree Tp and the null graph Oq , is studied. We prove that G is chromatically unique if and only if 1 < p < 3, 1 < q < 2; a graph H and Tp + Op-1 are x-equivalent if and only if H = Tp + Op-1, where Tp is a tree of order p; H and Tp +...
| Published in: | Прикладная дискретная математика № 50. С. 93-101 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Online Access: | http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000791059 Перейти в каталог НБ ТГУ |
| Summary: | The chromaticity of the graph G, which is join of the tree Tp and the null graph Oq , is studied. We prove that G is chromatically unique if and only if 1 < p < 3, 1 < q < 2; a graph H and Tp + Op-1 are x-equivalent if and only if H = Tp + Op-1, where Tp is a tree of order p; H and Tp + Op are x-equivalent if and only if H G {Tp + Op, TP+1 + Op-1}, where Tp is a tree of order p, Tp+1 is a tree of order p + 1. We also prove that if p < q, then xz(G) = ch'(G) = A(G); if A(G) = |V(G)| - 1, then x'(G) = ch'(G) = A(G) if and only if G = K3. |
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| Bibliography: | Библиогр.: 16 назв. |
| ISSN: | 2071-0410 |