hypohamiltonian graph
graph G is said to be hypohamiltonian if G does not itself have a Hamiltonian cycle but every graph formed by removing a single vertex from G is Hamiltonian
Coxeter graph
cubic distance-regular graph with 28 vertices and 42 edges
flower snark
infinite family of graphs
Petersen graph
cubic graph with 10 vertices and 15 edges
double-star snark
graph with 30 vertices and 45 edges