Unicyclic realizability of a degree list
Frank T. Boesch, Frank Harary · Networks · 1978
Abstract Simple necessary and sufficient conditions for a list of integers to be the degrees of the points of a tree are wellknown. Unicyclic graphs, which are connected graphs with exactly one cycle, are considered here. A simple set of necessary and sufficient conditions for a list of integers to be the degrees of the points of such a graph is derived.