Combinatorics and Graph Theory

1211 Submissions

[2] viXra:1211.0081 [pdf] submitted on 2012-11-14 10:59:09

Characterization of Partitions for Solid Graphs

Authors: Natasha Lee, Joan Portmann
Comments: 5 Pages.

The paper deals with the problems of characterization of simple graphical partitions belonging to the solid graphs, i.e. graphs, in which there are no four of vertices such that it is possible some shift of edges incidental to them and with characterization of the one class of steady graphs too. The necessary and sufficient conditions for the partition belonging to the solid graph have been established.
Category: Combinatorics and Graph Theory

[1] viXra:1211.0074 [pdf] submitted on 2012-11-13 09:11:35

Non-Solvable Ordinary Differential Equations With Applications

Authors: Linfan Mao
Comments: 46 Pages.

Different from the system in classical mathematics, a Smarandache system is a contradictory system in which an axiom behaves in at least two different ways within the same system, i.e., validated and invalided, or only invalided but in multiple distinct ways. Such systems exist extensively in the world, particularly, in our daily life. In this paper, we discuss such a kind of Smarandache system, i.e., non-solvable ordinary differential equation systems by a combinatorial approach, classify these systems and characterize their behaviors, particularly, the sum-stability and prod-stability of such linear and non-linear differential equations. Some applications of such systems to other sciences, such as those of globally controlling of infectious diseases, establishing dynamical equations of instable structure, particularly, the n-body problem and understanding global stability of matters with multilateral properties can be also found.
Category: Combinatorics and Graph Theory