A new upper bound on the number of edges in a geodetic graph (Q1301713)
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scientific article; zbMATH DE number 1334526
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new upper bound on the number of edges in a geodetic graph |
scientific article; zbMATH DE number 1334526 |
Statements
A new upper bound on the number of edges in a geodetic graph (English)
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29 November 1999
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A graph is geodetic if the shortest path between any pair of vertices is unique. It is a central geodetic block if each vertex is a center, whence it is 2-connected. It is proven that if in such a graph with \(p\) vertices, \(q\) edges and of diameter \(d\geq 3\), each vertex lies on a cycle of length \(2d+1\), then \(q=p\) or \(q\leq \frac{1}{6}p[p-\frac{1}{2}(5d+1)+8]\).
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central geodetic block
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number of edges
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upper bound
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