[7] **viXra:1309.0063 [pdf]**
*submitted on 2013-09-09 11:36:24*

**Authors:** Linfan Mao

**Comments:** 44 Pages.

Study of combinatorial spaces and smarandache multispaces.

**Category:** Combinatorics and Graph Theory

[6] **viXra:1309.0062 [pdf]**
*submitted on 2013-09-09 11:39:24*

**Authors:** Linfan Mao

**Comments:** 56 Pages.

This report survey the smarandache system, labeling graphs and others in the classical graph theory.

**Category:** Combinatorics and Graph Theory

[5] **viXra:1309.0061 [pdf]**
*submitted on 2013-09-09 11:41:53*

**Authors:** Linfan Mao

**Comments:** 56 Pages.

Combinatorial structures underlying things, Topology of Combinatorial Manifold, and Differentiationon Combinatorial Manifold are the topics of this paper.

**Category:** Combinatorics and Graph Theory

[4] **viXra:1309.0060 [pdf]**
*submitted on 2013-09-09 11:46:30*

**Authors:** Linfan Mao

**Comments:** 22 Pages.

An axiom is said smarandachely denied (S-denied)
if in the same space the axiom behaves differently,
i.e., validated and Invalided, or only invalidated
but in at least two distinct ways.
And a Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n≧2.
This paper studies them.

**Category:** Combinatorics and Graph Theory

[3] **viXra:1309.0059 [pdf]**
*submitted on 2013-09-09 11:48:05*

**Authors:** Linfan Mao

**Comments:** 27 Pages.

I will prescribe limitation on following topics and
mainly concentrate on myself works for combinatorially differential
geometry, particularly, the combinatorial counterpart in recent years.

**Category:** Combinatorics and Graph Theory

[2] **viXra:1309.0058 [pdf]**
*submitted on 2013-09-09 11:49:41*

**Authors:** Linfan Mao

**Comments:** 43 Pages.

Applications of Voltage Assignament
to Principal Fiber Bundles.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1309.0057 [pdf]**
*submitted on 2013-09-09 12:01:40*

**Authors:** Linfan Mao

**Comments:** 36 Pages.

We study the Smarandache Systems with Labeled Topological Graphs.
A rule R in a mathematical system (Sigma; R) is said to be Smarandachely denied if it behaves in at least two different ways within the same set Sigma, i.e. validated and invalided, or only invalided but in multiple distinct ways.
A Smarandache system (Sigma;R) is a system that has at least one smarandachely denied rule R.

**Category:** Combinatorics and Graph Theory