The line persistence of a graph G, p1 (G) is the minimum number of lines which must be removed to increase the diameter ......

The line persistence of a graph G, ρ1 (G) is the minimum number of lines which must be removed to increase the diameter......

A graph G is said to be an (ι,d)-graph (with respect to edges) if d(G-E) ≤ d, (∨)E (C) E(G) such that ∣E∣≤ι - 1. ......

In this paper we give a necessary and sufficient condition for a graph G with diameter 4 to be 3-diameter-stable.This re......