Characterizing symmetric diametrical graphs of order 12 and diameter 4
A diametrical graph G is said to be symmetric if d(u,v)+d(v,u¯)=d(G) for all u,v∈V(G), where u¯ is the buddy of u. If moreover, G is bipartite, then it is called an S-graph. It would be shown that the Cartesian product K2×C6 is not only the unique S-graph of order 12 and diameter 4, but also the uni...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202012474 |
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| author | S. Al-Addasi H. Al-Ezeh |
| author_facet | S. Al-Addasi H. Al-Ezeh |
| author_sort | S. Al-Addasi |
| collection | DOAJ |
| description | A diametrical graph G is said to be symmetric if d(u,v)+d(v,u¯)=d(G) for all u,v∈V(G), where u¯ is the buddy of u. If moreover, G is bipartite, then it is
called an S-graph. It would be shown that the Cartesian product
K2×C6 is not only the unique S-graph of order 12 and diameter 4, but also the unique symmetric diametrical
graph of order 12 and diameter 4. |
| format | Article |
| id | doaj-art-671cc80355674b279d74fb7278943caa |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-671cc80355674b279d74fb7278943caa2025-02-03T06:01:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0130314514910.1155/S0161171202012474Characterizing symmetric diametrical graphs of order 12 and diameter 4S. Al-Addasi0H. Al-Ezeh1Department of Mathematics, Hashemite University, Zarqa, JordanDepartment of Mathematics, University of Jordan, Amman, JordanA diametrical graph G is said to be symmetric if d(u,v)+d(v,u¯)=d(G) for all u,v∈V(G), where u¯ is the buddy of u. If moreover, G is bipartite, then it is called an S-graph. It would be shown that the Cartesian product K2×C6 is not only the unique S-graph of order 12 and diameter 4, but also the unique symmetric diametrical graph of order 12 and diameter 4.http://dx.doi.org/10.1155/S0161171202012474 |
| spellingShingle | S. Al-Addasi H. Al-Ezeh Characterizing symmetric diametrical graphs of order 12 and diameter 4 International Journal of Mathematics and Mathematical Sciences |
| title | Characterizing symmetric diametrical graphs of order
12 and diameter 4 |
| title_full | Characterizing symmetric diametrical graphs of order
12 and diameter 4 |
| title_fullStr | Characterizing symmetric diametrical graphs of order
12 and diameter 4 |
| title_full_unstemmed | Characterizing symmetric diametrical graphs of order
12 and diameter 4 |
| title_short | Characterizing symmetric diametrical graphs of order
12 and diameter 4 |
| title_sort | characterizing symmetric diametrical graphs of order 12 and diameter 4 |
| url | http://dx.doi.org/10.1155/S0161171202012474 |
| work_keys_str_mv | AT saladdasi characterizingsymmetricdiametricalgraphsoforder12anddiameter4 AT halezeh characterizingsymmetricdiametricalgraphsoforder12anddiameter4 |