Papers

The concepts like distance, eccentricity, radius etc. are very common in graph theory. Applying these concepts, Prajapati3 has designed a model to set up a fire station in a town. This paper is an extension of this idea and it deals with how can a public utility service in a certain region be made available to the various places in another region in the most democratic way. It also discusses at which place a public utility service shall be set up when two regions are connected by a bridge.

Given a graph G and a positive integer d, an L(d, 1)-labeling of G is a function f that assigns to each vertex of G a non-negative integer such that if two vertices u and v are adjacent, then f (u)  f (v)  d ; if u and v are not adjacent but there is a two-edge path between them, then f (u)  f (v )  1. The L(d, 1)-number of G,    d G , is defined as the minimum m such that there is an L(d, 1)-labeling f of G with f(V) {0, 1, 2,…, m}. Motivated by the channel assignment problem introduced by Hale, the L(2, 1)-labeling and the L(1, 1)-labeling (as d=2 and 1, respectively) have been studied extensively in the past decade. This article extends the study to all positive integers d.The aim of this paper is to determine the λd-number of the join of path and cycle and two graphs, Km + Pn and Km + Cn .

The evaluation of faculty performance plays a great role in monitoring and improving the performance of educational systems. Normally, the evaluation considers their contributions in teaching, research, and professional services. One of the common mechanisms for evaluating teaching performance is through a questionnaire that is distributed to students to express their opinions on the performance of their faculty. However, this questionnaire often contains vaguely defined linguisitic terms such as strong, competent, unsatisfactory, agree, strongly agree, etc. In this paper, we present a fuzzy assessment model to evaluate the teaching performance of faculty members from the data collected from their students. In this approach fuzzy sets are used to reperesent the impreciseness due to subjective judgements, and a fuzzy inference system is used to provide a crisp score for each faculty member.

This paper analyses the reliability of a cold standby system consisting of two repairable units and a server. At any time, one of the two units is operating while the other is on cold standby. The server takes some time to visit the system to do preventive maintenance and repair of the system. The preventive maintenance of the system is done by the server after a maximum operation time. The unit fails directly from the normal mode. The failure time of the unit follows negative exponential distribution while the distribution of preventive maintenance and repair times are taken as arbitrary. Repair and maintenance are perfect. The semi-Markov process and regenerative point technique is used to obtain expressions for various measures of system effectiveness. The behaviour of some important reliability measures has been observed graphically giving particular values to various costs and parameters.

Bernoulli’s numbers play an important role in mathematics and in various places like number theory, numerical analysis and differential topology. The aim of this paper is to provide a Computer program on Bernoulli numbers and their polynomials.

The Bernoulli polynomials have important applications in number theory and classical analysis. They appear in the integral
representation of differential periodic functions. Since they are employed for approximating such function in terms of polynomials³. The object of the present paper is to prove some basic properties of generalized Bernoulli polynomials.

In this paper,a new theorem on the degree of approximation of functions belonging to the class Lip((t),r) class by Euler and Matrix (E,q)A-product means of the Fourier series has been established.

A function f is called a graceful labelling of a graph G with q edges if f is an injection from the vertices of G to the set (0, 1, 2,..., q) such that, when each edge xy is assigned the label | f(x) — f(y)|, the resulting edge labels are distinct. A graph G is said to be one modulo N graceful (where N is a positive integer) if there is a function  from the vertex set
of G to {0, 1. N, (N + 1), 2N, (2N + 1),..., N(q - 1). N(q -1) + 1} in such a way that (i)  is 1-1 (ii)  induces a bijection * from the edge set of G to {1, N+1, 2N +1,..., N(q - 1)+1} where *(uv) = |(u) - (v)|. In this paper we prove that the acyclic graphs viz. Paths, Caterpillars, Stars and S2,n S2,n are one modulo N graceful for all positive integer N; Lobsters, Banana trees and Rooted tree of height two are one modulo N graceful for N > 1. where Sm,n Sm,n is a graph obtained by identifying one pendant vertex of each Sm,n. This is a fire cracker of subdivisioned stars.

Within this paper, subspace questions are further investigated for compact spaces, hereditarily compact spaces, and T0 spaces using closed set subspaces and open set subspaces.

The semientire edge dominating graph Eed(G) of a graph G=(V, E) is a graph with the vertex set E S where S is the set of
all minimal edge dominating sets G and with two vertices u,v E S adjacent if u,v F where F is a minimal edge dominating set in S or u E and v=F is a minimal edge dominating set of G containing u. In this paper, a characterization is given for graphs G for which Eed(G) is connected. Further, some new results are established relating to this new graph.