Saturation Numbers of Books

A book Bp is a union of p triangles sharing one edge. This idea was extended to a generalized book Bb,p, which is the union of p copies of a Kb+1 sharing a common Kb. A graph G is called an H-saturated graph if G does not contain H as a subgraph, but G∪ {xy} contains a copy of H, for any two nonadjacent vertices x and y. The saturation number of H, denoted by sat(H,n), is the minimum number of edges in G for all H-saturated graphs G of order n. We show that sat(Bp, n) = 1 2 ( (p + 1)(n − 1) − ⌈p 2 ⌉ ⌊p 2 ⌋