The forcing geodetic number of a graph
Gary Chartrand, Ping Zhang · Discussiones Mathematicae Graph Theory · 1999
For two vertices u and v of a graph G, the set I(u, v) consists of all vertices lying on someS is the minimum cardinality among the forcing subsets of S, and the forcing geodetic number f (G) of G is the minimum forcing geodetic number among all minimum geodetic sets of G.The forcing geodetic numbers of several classes of graphs are determined.For every graph G, f (G) ≤ g(G).It is shown that for all integers a, b with 0 ≤ a ≤ b, a connected graph G such that f (G) = a and g(G) = b exists if and only if (a, b) / ∈ {(1, 1), (2, 2)}.