A general class of invulnerable graphs
Frank T. Boesch, Alan Felzer · Networks · 1972
Abstract The idea of utilizing the connectivity properties of a graph as measures of its vulnerability has been well documented. The graph theoretic concepts and the basic results of this theory are reviewed here. Various types of optimally invulnerable graphs are defined and compared. New results are presented for the synthesis of optimal graphs. Specifically a class of graphs called telescopically non‐contracting star polygons are shown to constitute a rather general set of invulnerable graphs. This new class extends the set of known optimal graphs considerably.