I was working out on a problem. Came out with a result in $C_n$: radius = diam. Worked out on other few graphs where radius=diam. Can we generalize the result? A little hint will be helpful. The examples on which I worked out, turned out to be regular too. Thanks
2026-04-15 10:27:21.1776248841
The graphs in which radius is equal to diameter
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The obvious family of such graphs are vertex transitive graphs. All vertex transitive graphs are self-centered (every vertex has the same eccentricity). Their complements are also vertex transitive graphs and thus are also self-centered. These will always be regular graphs, however.