iosr-Jm   International Conference on Emerging Trends in Engineering and Management (ICETEM-2016)

Abstract:Let G be a simple connected graph with n vertices and m edges. The mycielski graph  (G) of
G contains G itself as an isomorphic subgraph, together with n 1 additional vertices : a vertex i u
corresponding to each vertex i v of G and another vertex w. Each vertex i u connected by an edge to w, so
that these vertices form a subgraph in the form of a star n K , 1 . In addition, for each edge ( , ) i j v v of G , the
mycielski graph includes two edges ( , ) i j u v and ( , ) j vi u . In this paper we obtain First Zagreb index, First
Zagreb Eccentricity index, Eccentric connectivity indices and polynomials and connective eccencticity index for
the complement of Mycielski graphs. Furthermore, upper and lower bounds for the Harmonic index is also
provided.

[1] M. Caramia and P. Dell ' olmo, A lower bound on the chromatic number of Mycielski graphs, creteMathematics, Vol.235(2001),
pp. 79  86.
[2] G.J. Chang, L. Huang and X. Zhu, Circular chromatic numbers of Mycielski ' s graphs, Discrete Mathematics, Vol.205(1994), pp.
23  37.
[3] V. Chva ' tal, The Minimality of the Mycielski graph, Lecture Notes in Mathematics, Vol.406(1974), p. 243  246.
[4] K.L. Collins and K. Tysdal, Dependant edges in Mycielski graphs and 4  colorings of 4  skeletons, Journal of Graph Theory,
Vol.46(2004), pp. 285  296.
[5] H. Hua, A.R. Ashrafi and L. Zhang, More on Zagreb Coindices of graphs, Filomat 26 : 6(2012), pp. 1215  1225.
[6] M. Eliasi, G. Raeisi and B.Taeri, Wiener index of some graph operations, Discrete Applied Mathematics, Vol.160(2012), p. 1333
 1344.
[7] S. Fajtlowicz, On conjectures of Graffiti- II, Congr. Numer., Vol.60(1987), pp. 187-197.

Abstract: Growth rate computation relating to the performance of an economy is usually is based on positive values of a time-dependent variable. There is a constraint to compute growth rate when such a variable is consistently negative. This paper makes an enquiry into the possibility of using a method to overcome this constraint, which is not very popular in India. Key words: Growth rate, negative growth,logarithmic transformation, time-dependent variable, Current account deficit, reverse of a time-dependent negative variable.

[1] Goldberg, and Richard R, Methods of Real Analysis (John Wiley & sons, New York, 1976). [2] Ray, and Debraj, Development Economics (Oxford University Press, London, 1998). [3] Economic Survey, 2012-13, (Government of India, Oxford, New Delhi, 2013) [4] Sodersten, Bo and Geoffrey Reed, International Economics (Macmillan, New Delhi, 1994). [5] Gujarati, Damodar N, Dawn C Porter and Sangeetha Gunasekhar, Basic Econometrics (McGraw Hill Education, India, 2012).

Abstract:Let G : (V, E, ω) be a finite, connected, weighted graph without loops and multiple edges. In a
weighted graph each arc is assigned a weight by the weight function ω: E  . A u−v path P in G is called a
weighted u−v geodesic if the weighted distance between u and v is calculated along P. The strength of a path is
the minimum weight of its arcs, and length of a path is the number of edges in the path. In this paper, we
introduce the concept of weighted geodesic convexity in weighted graphs. A subset W of V (G) is called
weighted geodetic convex if the weighted geodetic closure of W is W itself. The concept of weighted geodetic
blocks is introduced and discussed some of their properties. The notion of weighted geodetic boundary and
interior points are included.
Keywords - intervals in graph, geodesic, graph convexity,

[1] J. A. Bondy, and G. Fan, Cycles in weighted graphs, Combinatorica, 11, 1991, 191-205. [2] J. A. Bondy, and G. Fan, Optimal paths and cycles in weighted graphs , Ann. Discrete Mathematics 41, 1989, 53- 69. [3] F. Buckley and F. Harary, Distance in Graphs (Addision-Wesley, Redwood City, CA, 1990). [4] Sunil Mathew, and M. S. Sunitha, Some connectivity concepts in weighted graphs, Advances and Applications in Discrete Mathematics 6(1), 2010, 45-54. [5] Sunil Mathew, M. S. Sunitha and Anjaly N., Some connectivity concepts in bipolar fuzzy graphs, Annals of Pure and Applied Mathematics, 7(2), 2014, 88-108. [6] Jill K. Mathew, and Sunil Mathew, Weighted distance in graphs, Proceedings of NCMSC-2012, 129-132. [7] Jill K. Mathew, and Sunil Mathew, Some extremal Problems in weighted graphs, Annals. of Pure and Applied Mathematics, 8(1), 2014, 27-37.

Abstract:Fuzzy multi objective linear programming problem has its application in a variety of research and development field. It is the application of fuzzy set theory in linear decision making problem. In this paper, solution procedure of multi objective fuzzy linear programming with triangular membership function is presented. With the help of numerical example the method is illustrated. Keywords : Fuzzy Linear Programming, Fuzzy number , Optimal solution, pareto optimality, Triangular Fuzzy number .

[1] R.E. Bellman, and L.A. Zadeh, Decision making in a fuzzy environment, Management Science 17,1970 141-164. [2 ] D. Chanas, Fuzzy programming in multi objective linear Programming-a parametric approach, Fuzzy Set and system ,29 ,1 989 303-313. [3] H. Ishibuchi H. Tanaka Multi-objective programming in optimization of the interval objective function, European Journal of Operational Research , 48, 1990, 219-225. [4] H., Tanaka ,and K., Asai, Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets and Systems, 13, 1984, 1-10. [5] H.J., Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy sets and System , 1978, 45- 55. [6] S.H.Nasseri, A New Method for Solving Fuzzy Linear Programming by Solving Linear Programming. Applied Mathematics sci., 2(50), 2008, 2473-2480.