On Almost Self-centered Graphs and Almost Peripheral Graphs
On Almost Self-centered Graphs and Almost Peripheral Graphs
An almost self-centered graph is a connected graph of order $n$ with exactly $n-2$ central vertices, and an almost peripheral graph is a connected graph of order $n$ with exactly $n-1$ peripheral vertices. We determine (1) the maximum girth of an almost self-centered graph of order $n$; (2) the maximum …