On even graphs
A nontrivial connected graph G is called even if for each vertex v of G there is a unique vertex v' such that d(v, v') = diam G = d. Special classes of even graphs are defined and compared to each other specifically that of symmetric even graph which has the following property: d(u, v) + d...
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| Format: | text |
| Language: | English |
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Animo Repository
1998
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_masteral/1955 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | A nontrivial connected graph G is called even if for each vertex v of G there is a unique vertex v' such that d(v, v') = diam G = d. Special classes of even graphs are defined and compared to each other specifically that of symmetric even graph which has the following property: d(u, v) + d(u, v') = d for all u, v e V(G). Several properties of even and symmetric even graphs are included. For an even graph of order n and diameter d other than an even cycle, it is shown that n is equal to or greater than 3d-1. Moreover, for a symmetric even graph order n and diameter d, it is shown that n is equal to or greater than 4d-4. |
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