Enumeration of the Degree Sequences of Line–hamiltonian Multigraphs
نویسندگان
چکیده
Recently, Gu, Lai and Liang proved necessary and sufficient conditions for a given sequence of positive integers d1, d2, . . . , dn to be the degree sequence of a line– Hamiltonian multigraph. Our goal in this note is to utilize this result to prove a closed formula for the function dlh(2m), the number of degree sequences with degree sum 2m representable by line–Hamiltonian multigraphs. Indeed, we give a truly elementary proof that dlh(2m) = p(2m)− 2 m−1 ∑
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