The size of graphs uniquely Hamiltonian-connected from a vertex (Q1078574)

A graph G is called uniquely Hamilton-connected (UHC) from a vertex v of G if G contains exactly one v-u Hamiltonian path for each vertex u,u\(\neq v\). The main result of the paper is the following theorem: if G is a graph of order n (n\(\geq 5)\) which is UHC-graph from v, then G has exactly (3n-3)/2 edges. A number of properties of UHC-graphs from a vertex are deduced from the theorem.