The polynomial we consider here is the characteristic polynomial of a certain (not adjacency) matrix associated with a graph. This polynomial was introduced in connection with the problem of counting spanning trees in graphs . In the present paper the properties of this polynomial are used to construct some classes of graphs with an extremal numbers of spanning trees. © 1974.
Kelmans, A. K., & Chelnokov, V. M. (1974). A certain polynomial of a graph and graphs with an extremal number of trees. Journal of Combinatorial Theory, Series B, 16(3), 197–214. https://doi.org/10.1016/0095-8956(74)90065-3