Mathematics

Dalfo, C.; van Dam, E.R.; Fiol, M.A.; Garriga, E.; Gorissen, Bram Abstract Distance-regular graphs have been a key concept in Algebraic Combinatorics and have given place to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study 'almost distance-regular graphs'. We use this name informally for graphs that share some regularity properties that are related to distance in the graph. For example, a known characterization of a distance-regular graph is the invariance of the number of walks of given length between vertices at a given distance, while a graph is called walk-regular if the number of closed walks of given length rooted at any given vertex is a constant. One of the concepts studied here is a generalization of both distance-regularity and walk-regularity called m-walk-regularity. Another studied concept is that of m-partial distance-regularity, or informally, distance-regularity up to distance m. Using eigenvalues of graphs and the predistance polynomials, we discuss and relate these and other concepts of almost distance-regularity, such as their common generalization of ( , m)-walk-regularity. We introduce the concepts of punctual distance-regularity and punctual walk-regularity as a fundament upon which almost distance-regular graphs are built. We provide examples that are mostly taken from the Foster census, a collection of symmetric cubic graphs. Two problems are posed that are related to the question of when almost distance-regular becomes whole distance-regular. We also give several characterizations of punctually distance-regular graphs that are generalizations of the spectral excess theorem.

In this paper, Beta product and Gamma product of two fuzzy graphs are introduced and we proved that the Beta product of two regular fuzzy graphs need not be regular and that if G 1 × β G 2 is regular, then G 1 (or) G 2 need not be regular. A necessary and sufficient condition for G 1 × β G 2 and G 1 × γ G 2 to be a regular fuzzy graph is determined. The degree of vertices in G 1 × β G 2 and G 1 × γ G 2 in terms of those in G 1 and G 2 are determined for some particular cases and regular property of G 1 × β G 2 and G 1 × γ G 2 are studied.

In this paper, Beta product and Gamma product of two fuzzy graphs are introduced and we proved that the Beta product of two regular fuzzy graphs need not be regular and that if G 1 × β G 2 is regular, then G 1 (or) G 2 need not be regular. A necessary and sufficient condition for G 1 × β G 2 and G 1 × γ G 2 to be a regular fuzzy graph is determined.

Abstract. In this paper, Beta product and Gamma product of two fuzzy graphs are introduced and we proved that the Beta product of two regular fuzzy graphs need not be regular and that if G1×β G2 is regular, then G1 (or) G2 need not be regular. A necessary and sufficient condition for G1×β G2 and G1× γ G2 to be a regular fuzzy graph is determined.

In this paper we will present some basic concepts of network analysis. We will present some key aspects of network analysis on analysis of social network. These methods are used to simulate the properties observed in biological networks as well. We also will present some algorithms used in of biological networks modeling. In all computation we will shortly present the toolbox used for pathway analysis FluxAnalyser [1] which uses MATLAB environment and which is the toolbox we mostly use in our analyses of some networks.

In this paper we will present some basic concepts of network analysis. We will present some key aspects of network analysis on analysis of social network. These methods are used to simulate the properties observed in biological networks as well. We also will present some algorithms used in of biological networks modeling. In all computation we will shortly present the toolbox used for pathway analysis FluxAnalyser [1] which uses MATLAB environment and which is the toolbox we mostly use in our analyses of some networks.

In this paper, we present the study of the two-parameter Weibull distribution theory and its parameters (shape β and scale α) using Weibull Probability Plotting. Using the failure data for haul trucks in operation at a marble quarry, we obtain the fatigue life equation by regression under different failure probabilities. Weibull distribution analysis for reliability and maintainability is showing a tendency of increasing failure rate, leaving room for decisions on reliability centered maintenance planning, machine improvements, optimal load and the need for review of data collection process.

This paper presented the estimation of system reliability using two parameter Weibull distribution. The parameters are estimated using Weibull probability plot & statistical analysis and the results being presented in charts. An increasing complexity of systems often leads to an increase of failure mechanisms. A statistical analysis of the lifetime of systems with several failure mechanisms consisting of several subcomponents considered The Weibull distribution is commonly used as a lifetime distribution in reliability applications. The two-parameter Weibull distribution can represent a decreasing, constant or increasing failure rate.

This paper focuses on a case study to estimate the reliabilities of two competing machines, when the only available data is Time To Failure. The Weibull Parameters are calculated using Microsoft Excel 2010. The results show that after knowing the reliabilities of both the Bulldozers at different lengths of time, we can ascertain which of them is preferable to use at which time period. Study of reliabilities of machinery used in any kind of production is of utmost necessity for optim um use of man power and resources to make the process cost effective and with minimum downtime. This is applicable for all large and small industries alike. But in small industries data is not accurately stored and it becomes difficult to estimate product reliabilities.

We study on energy homeostasis ensures the functionality of the entire organism. The human brain as a missing link in the global regulation of the complex whole body energy metabolism is subject to recent investigation. The goal of this study is to gain insight into the influence of neuronal brain activity on cerebral and peripheral energy metabolism. In particular, the tight link between brain energy supply and metabolic responses of the organism is of interest. We aim to identifying regulatory elements of the human brain in the whole body energy homeostasis.

On the basis of well known B-model a cummulative damage model is introduced. The model is based on fracture mechanics
hence named as FM-model. The objective of the paper is to relate the basic idea of B-model in such a way so as to transfer
results from one structure to another. The accounts of the geometry of structure is taken through stress intensity fator. The
model is applicable in wider sense both deterministic as well as to random loading

In this paper, is to permit the system reliability analysts/managers/engineers/ practitioners to conduct RAM analysis of the system which may help them to model, analyze and predict the behavior of industrial systems in a more realistic and consistent manner. Markovian approach is used to model the system behavior. For carrying out study, Root Cause Analysis (RCA) of the subsystems is carried out and transition diagrams for various subsystems are drawn and differential equations associated with them are formulated. After obtaining the steady state solution the corresponding values of reliability and maintainability are estimated at different mission times. With RAM analysis of the system key performance metrics such as Mean Time between Failure (MTBF), Mean time to Repair Time (MTTR) and System availability values are ascertained.

In this paper, mixed dominating set, mixed domination number , mixed strong domination number and mixed weak domination number of an M-strong fuzzy graph G = (σ, µ) are defined. Also these numbers are determined for various standard fuzzy graphs. The relationship between these numbers and other well known numbers are derived.

A subset S of V in a graph G = (V, E) is called an equal eccentric dominating set(eed-set) if S is a dominating set and ∀ y ∈ V − S, ∃ at least one equal eccentric vertex x of y in S. In this paper, equal eccentric vertex, equal eccentric set, equal eccentric dominating set and equal eccentric domination numbers are defined. The equal eccentric domination numbers of various standard graphs are obtained and the bounds on equal eccentric domination numbers are also obtained and theorems related to this concepts are stated and proved.