[3] **viXra:1601.0247 [pdf]**
*submitted on 2016-01-22 21:57:43*

**Authors:** Quang Nguyen Van

**Comments:** 14 pages. We have other one written in tex.file

We choose one of four colors as a temporary color for all regions that have not been colored,and made the initial conditions corresponding to The Four Color Theorem. If these conditions hold for any n regions figure, then they will hold for n + 1 regions figure - formed n regions figure by adding next region. By induction, step by step we have proved The Four Color theorem successfully on paper (in 2015).

**Category:** Combinatorics and Graph Theory

[2] **viXra:1601.0200 [pdf]**
*replaced on 2016-01-30 07:39:24*

**Authors:** Prashanth R. Rao

**Comments:** 3 Pages.

In a previous paper we described a method to represent graph information as a single numerical value by distinctly labeling each of its vertices with unique primes. In this paper, we modify the previous approach to again represent a graph as a single numeric value, we log transform this value and approximate it with an optimum value which if minimized by appropriate prime labeling of the graph should allow us to compare it with another graph on which an identical algorithm is implemented. Identical optimum value minima is a necessary but not sufficient condition for graph isomorphism.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1601.0048 [pdf]**
*submitted on 2016-01-06 05:30:54*

**Authors:** Quang Nguyen Van

**Comments:** 5 Pages.

We introduce an efficient method for exporting a sequence of prime numbers by using Excel.

**Category:** Combinatorics and Graph Theory