# Combinatorics and Graph Theory

## 1210 Submissions

[3] **viXra:1210.0161 [pdf]**
*submitted on 2012-10-27 09:09:57*

### Binomial Construction of the Trinomial Triangle

**Authors:** Martin Erik Horn

**Comments:** 17 Pages.

The trinomial triangle can be constructed in a binomial way using unit vectors of geometric algebra of quarks. This sheds some light on the question, how it is possible to transform mathematically entities of two elements into entities of three elements or vice versa.

**Category:** Combinatorics and Graph Theory

[2] **viXra:1210.0081 [pdf]**
*submitted on 2012-10-16 23:30:24*

### Probe Graph Classes

**Authors:** D. B. Chandler, M.-S. Chang, T. Kloks, J. Liu, S.-L. Peng

**Comments:** 121 Pages.

Let GG be a class of graphs. A graph G is a probe graph of GG if its vertex set can be partitioned into a set P of `probes' and an independent set N of `nonprobes' such that G can be embedded into a graph of GG by adding edges between certain nonprobes.
In this book we investigate probe graphs of various classes of graphs.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1210.0049 [pdf]**
*submitted on 2012-10-10 05:51:51*

### In an Adjacency Matrix Which Encodes for a Directed Hamiltonian Path, a Non-Zero Determinant Value Certifies the Existence of a Directed Hamiltonian Path When no Zero Rows (Columns) and no Similar Rows (Columns) Exist in the Adjacency Matrix

**Authors:** Okunoye Babatunde O.

**Comments:** 6 Pages.

The decision version of Directed Hamiltonian path problem is an NP-complete problem which asks, given a directed graph G, does G contain a directed Hamiltonian path? In two separate papers, the author expresses the graph problem as an adjacency matrix and a proof given to show that under two special conditions relating to theorems on the determinant of a square matrix, a non-zero determinant value certifies the existence of a directed Hamiltonian path. Here, a brief note is added to repair a flaw in the proof. The result, as expressed in the paper title is a more defensible proposition

**Category:** Combinatorics and Graph Theory