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Graphs related to diameter and center. (English) Zbl 0922.05023
Summary: A graph is said to be an $$L$$-graph if all its paths of diametral length contain a central vertex of $$G$$. Using an earlier result we show that any graph can be embedded to an $$L$$-graph of radius $$a$$ and diameter $$b$$, where $$a \leq b \leq 2a$$. We show that the known bounds of the number of edges and the maximum degree of the graphs of diameter $$d \leq 2$$ are sharp for $$L$$-graphs, too. Then we estimate the minimum degree of $$L$$-graphs. Finally we estimate the number of central vertices in $$L$$-graphs; all bounds are best possible.
##### MSC:
 05C12 Distance in graphs 05C35 Extremal problems in graph theory
##### Keywords:
center; $$L$$-graph; radius; diameter; bounds; maximum degree
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