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1 Introduction
1 Introduction
This paper contains examples of various features from AMS-LATEX.
This paper contains examples of various features from AMS-LATEX.
2 Enumeration of Hamiltonian paths in a graph
2 Enumeration of Hamiltonian paths in a graph
Letbe the adjacency matrix of graph. The corresponding Kirchhoff
Let bold A equals open paren a sub i j close paren be the adjacency matrix of graph G. The corresponding Kirchhoff
matrixis obtained fromby replacing ineach diagonal entry by the
matrix bold K equals open paren k sub i j close paren is obtained from bold A by replacing in negative bold A each diagonal entry by the
degree of its corresponding vertex; i.e., theth diagonal entry is identified with the
degree of its corresponding vertex; i.e., the ith diagonal entry is identified with the
degree of theth vertex. It is well known that
degree of the ith vertex. It is well known that
the determinant of bold K of open paren i divides i close paren equals the number of spanning trees of G comma i equals 1 comma period period period comma n