Applied Mathematics

A set D of vertices in a graph G = (V, E) is called a dominating set of G, if every vertex in V-D is adjacent to some vertex in D. The domination number (G) of G is the minimum cardinality of a dominating set in G. A dominating set D of a graph G is a complementary tree dominating set, if the induced subgraph is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of G and is denoted by ctd(G).The chromatic number of G is the minimum number of colours assigned to the vertices of G such that no two adjacent vertices have the same colour and is denoted by (G).In this paper we investigate cubic graphs for which ctd(G) = (G).

In conventional assignment problem, cost is always certain. In this paper, Assignment problem with crisp, fuzzy and intuitionistic fuzzy numbers as cost coefficients is investigated. There is no systematic approach for finding an optimal solution for mixed intuitionistic fuzzy assignment problem. This paper develops an approach to solve a mixed intuitionistic fuzzy assignment problem where cost is not in deterministic numbers but imprecise ones. The solution procedure of mixed intuitionistic fuzzy assignment problem is proposed to find the optimal assignment and also obtain an optimal value in terms of triangular intuitionistic fuzzy numbers. Numerical examples show that an intuitionistic fuzzy ranking method offers an effective tool for handling an intuitionistic fuzzy assignment problem.

In this paper, we made an attempt to study the algebraic nature of anti S-fuzzy subfield of a field.

In this paper the symmetry classification of third order quasi-linear PDE's containing arbitrary function have been studied with derailed examples.

Risk assessment is an important and more popular aid in decision making process. Risk assessment is generally performed using models and model is a function of some parameters which are usually affected by uncertainty. Here, we consider that the model parameters are affected by epistemic uncertainty. To represent epistemic uncertainty generally triangular fuzzy numbers or trapezoidal fuzzy numbers are used. In this paper, Cauchy fuzzy number together with triangular fuzzy numbers is used to represent epistemic type uncertainty. An effort has been made to fuse Cauchy fuzzy number with triangular fuzzy number and then human health risk assessment is carried out under fuzzy environment.

The main objective of present investigation is to introduce the magnetohydrodynamic peristaltic transport with porous medium through a coaxial asymmetric vertical tapered channel and Joule heating with radiation. Effects of sundry parameters on the temperature and heat transfer coefficient at the wall y = h1 are studied through graphs. It is noted that the temperature increases when increase in Radiation parameter (N), Prandtl number (Pr), heat source/sink parameter (?), Brinkman number (Br), Hartmann number (M), non-uniform parameter (K1) and non-dimensional amplitude (?) in entire tapered channel. Further, we observe that the heat transfer coefficient decreases when non-uniform parameter (K1) is assigned higher values.

Let G be a graph with n vertices. Prime labeling of G is the labeling of the vertices using first n positive integers such that labeling of each pair of adjacent vertices are relatively prime. This work is a generalization of [2] which was analogous to [1] in which prime labeling for complete bipartite graphs were considered. In [2] conditions for the existence of prime labeling of complete tripartite graphs of the form K_(1,m,n) was given where m,n?Z^+. In our work, we have proved that prime labeling of K_(2,m,n) and K_(3,m,n) exists for some values of m and n where m,n?Z^+. Further, few non-existance cases have been discussed.

We consider a singular Sturm-Liouville differential expression with an indefinite weigh and present a sufficient condition for similarity of indefinite Sturm-Liouville operators to self- adjoint operators. Using this result, we construct a example of operator and prove that it is similar to a self-adjoint one.

The aim of this paper is to develop a methodology for solving matrix games with fuzzy payoffs. Here, a fuzzy matrix game has been considered and its solution method has been proposed using interval parametric technique. This technique is based on parametric representation of interval number. In this technique, the fuzzy number has been converted into interval number using interval approximation of fuzzy number and the interval number has been presented to its parametric interval functional form. Then the corresponding matrix game has been converted into crisp game using the said technique. The value of the matrix game for each player is obtained by solving corresponding crisp game problems using the existing method. Finally, a numerical example has been considered and solved in support of the solution method.

The solution of the problem of slow flow of an incompressible viscous fluid past a porous sphere with solid pore embedded in another porous medium is investigated. The Brinkman equation for the flow inside and outside the porous sphere in their stream function formulation is used. Explicit expressions are investigated for stream function, shear stress and normal stress for inside and outside region. The drag force experienced by a porous sphere with solid pore embedded in a porous medium is also evaluated.