[6] **viXra:1602.0157 [pdf]**
*submitted on 2016-02-13 11:02:28*

**Authors:** Mohamed Eleiche

**Comments:** 12 Pages.

The minimum-travel-cost algorithm is a dynamic programming algorithm to compute an exact and deterministic lower bound for the general case of the traveling salesman problem (TSP). The algorithm is presented with its mathematical proof and asymptotic analysis. It has a (n2) complexity. A program is developed for the implementation of the algorithm and successfully tested among well known TSP problems.

**Category:** Combinatorics and Graph Theory

[5] **viXra:1602.0153 [pdf]**
*submitted on 2016-02-13 09:00:10*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

The science's function is realizing the natural world, developing our society in coordination with natural laws and mathematics provides the quantitative tool and method for solving problems helping with that understanding. Generally, understanding a natural thing by mathematical ways or means to other sciences are respectively establishing mathematical model on typical characters of it with analysis first, and then forecasting its behaviors, and finally, directing human beings for hold on its essence by that model.

**Category:** Combinatorics and Graph Theory

[4] **viXra:1602.0121 [pdf]**
*submitted on 2016-02-10 11:59:09*

**Authors:** Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache

**Comments:** 33 pages

The notion of interval valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets, interval valued fuzzy sets, interval valued intuitionstic fuzzy sets and single valued neutrosophic sets. We apply for the first time the concept of interval valued neutrosophic sets, an instance of neutrosophic sets, to graph theory. We introduce certain types of interval valued neutrosophc graphs (IVNG) and investigate some of their properties with proofs and examples.

**Category:** Combinatorics and Graph Theory

[3] **viXra:1602.0120 [pdf]**
*submitted on 2016-02-10 12:02:44*

**Authors:** Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache

**Comments:** 21 pages

In this paper, we discuss a subclass of interval valued neutrosophic graphs called strong interval valued neutrosophic graphs which were introduced by Broumi et al [41]. The operations of Cartesian product, composition, union and join of two strong interval valued neutrosophic graphs are defined. Some propositions involving strong interval valued neutrosophic graphs are stated and proved.

**Category:** Combinatorics and Graph Theory

[2] **viXra:1602.0117 [pdf]**
*submitted on 2016-02-10 06:26:54*

**Authors:** Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache

**Comments:** 16 pages

The notion of single valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets. We apply the concept of single valued neutrosophic sets, an instance of neutrosophic sets, to graphs. We introduce certain types of single valued neutrosophic graphs (SVNG) and investigate some of their properties with proofs and examples.

**Category:** Combinatorics and Graph Theory

[1] **viXra:1602.0076 [pdf]**
*submitted on 2016-02-06 11:00:18*

**Authors:** Many Authors

**Comments:** 145 Pages.

Collection of papers on combinatorics.

**Category:** Combinatorics and Graph Theory