Enumeration of labeled connected graphs with k cycles is an open problem . Up to now it has been settled only for k = 1, 2. Unfortunately , these given for-mulas are very complicated . In this paper we improve a serie...Enumeration of labeled connected graphs with k cycles is an open problem . Up to now it has been settled only for k = 1, 2. Unfortunately , these given for-mulas are very complicated . In this paper we improve a series of enum nerations and solve the enumeration problem for k = 3.展开更多
In (I), hypertrees and uniform hypertrees are enumerated. Continuing the work of (I), the authors consider the problem of enumeration of hypertrees with constrains to extend Clarke's formula, Moon's formula, T...In (I), hypertrees and uniform hypertrees are enumerated. Continuing the work of (I), the authors consider the problem of enumeration of hypertrees with constrains to extend Clarke's formula, Moon's formula, Temperley's formula, Weinberg's formula and O'Neil's formula of simple labeled trees to hypertrees.展开更多
Let the coronas C<sub>n</sub>⊙K<sub>1</sub> be the polygons with one additional end-point for eachvertex.Thom Grace conjectured that C<sub>n</sub>⊙K<sub>1</sub> are ha...Let the coronas C<sub>n</sub>⊙K<sub>1</sub> be the polygons with one additional end-point for eachvertex.Thom Grace conjectured that C<sub>n</sub>⊙K<sub>1</sub> are harmonious for n even.In this paper,aproof of his conjecture is given.展开更多
Let G=(V(G), E(G)) be a simple graph with p vertices and q edges. A labeling g is a one-to-one mapping from V(G) to the positive integers. Then G is said to be harmonious if it is possible to label the vertices of G w...Let G=(V(G), E(G)) be a simple graph with p vertices and q edges. A labeling g is a one-to-one mapping from V(G) to the positive integers. Then G is said to be harmonious if it is possible to label the vertices of G with distinct elements Of Z_q (the integers modulo q)in such a way that, when each edge(u, v)is labeled with g(u)+g(v)展开更多
文摘Enumeration of labeled connected graphs with k cycles is an open problem . Up to now it has been settled only for k = 1, 2. Unfortunately , these given for-mulas are very complicated . In this paper we improve a series of enum nerations and solve the enumeration problem for k = 3.
文摘In (I), hypertrees and uniform hypertrees are enumerated. Continuing the work of (I), the authors consider the problem of enumeration of hypertrees with constrains to extend Clarke's formula, Moon's formula, Temperley's formula, Weinberg's formula and O'Neil's formula of simple labeled trees to hypertrees.
文摘Let the coronas C<sub>n</sub>⊙K<sub>1</sub> be the polygons with one additional end-point for eachvertex.Thom Grace conjectured that C<sub>n</sub>⊙K<sub>1</sub> are harmonious for n even.In this paper,aproof of his conjecture is given.
文摘Let G=(V(G), E(G)) be a simple graph with p vertices and q edges. A labeling g is a one-to-one mapping from V(G) to the positive integers. Then G is said to be harmonious if it is possible to label the vertices of G with distinct elements Of Z_q (the integers modulo q)in such a way that, when each edge(u, v)is labeled with g(u)+g(v)
