EdgeCoverQ
EdgeCoverQ[g, elist] yields True if the edge list elist is an edge cover of the graph g and False otherwise.
Examples
Check if edges cover all vertices:
EdgeCoverQ[CycleGraph[4], {1 <-> 2, 3 <-> 4}]
(* True *)Incomplete cover:
EdgeCoverQ[PathGraph[Range[5]], {1 <-> 2}]
(* False *)Please visit the official Wolfram Language Reference for more details.