iosr-Jm   International Conference on Emerging Trends in Engineering and Management (ICETEM-2014)

Abstract:paper we present the ABC index of subdivision graphs of some connected graphs.We also provide the ABC index of the line graphs of some subdivision graphs
Keywords: Atom-bond connectivity(ABC) index, Subdivision graph, Line graph, Helm graph, Ladder graph, Lollipop graph.

[1]. Das, K.C. Atom-bond Connectivity index of graphs, Discrete Applied Mathematics, Vol. 158 (2010) pp. 1181 - 1188.
[2]. Estrada, E. Atom-bond connectivity and the energetic of branched alkanes, Chem. Phys. Lett. Vol. 463 (2008), pp. 422 - 425.
[3]. Estrada,E., Torres, L., Rodríguez, L., and Gutman, I. An atom-bond connectivity index: modelling the enthalpy of formation of alkanes, Indian J. Chem., Vol. 37 (1998), pp. 849- 855.
[4]. Furtula, B., Graovac, A., and Vuki£evic, D. Atom-bond connectivity index of trees, Discrete Appl. Math. Vol.157 (2009), pp. 2828 - 2835.
[5]. Hosseini, S. A., Ahmadi, M.B., and Gutman, I. Kragujevac trees with minimal atom - bond connectivity index, MATCH Commun. Math. Comput. Chem., Vol. 71(2014), pp. 5 - 20.
[6]. Pemmaraju, S., and Skiena, S. Cycles, Stars, and Wheels, Computational Discrete Mathematics. Graph Theory in Mathematica. Cambridge, England: Cambridge university press, Vol. 6, pp. 248 - 249.

Abstract:In a weighted graph, the arcs are mainly classified into ,  and . In this article, some new distances and sequences in weighted graphs are introduced. These concepts are based on the above classification. With respect to the distances, the concepts of centre and self centered graphs are introduced and their properties are discussed. It is proved that, only partial blocks with even number of vertices can be self centered. Using the sequences, a characterization for partial blocks and precisely weighted graphs (PWG) are obtained.
Keywords –  distance,  distance, partial blocks, partial trees, PWG.

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[9] Sunil Mathew, M. S. Sunitha, On totally weighted interconnection networks, Journal of interconnection networks 14,(2010).

[10] Sunil Mathew, M. S. Sunitha, Some Connectivity concepts in weighted graphs, Advances and Applications in Discrete Mathematics 6(1), pp. 45-54 (2010).

Abstract:Under some restrictions, a global solution  of the Poisson equation  can be constructed in Euclidean Spaces, Riemann surfaces, Brelot harmonic spaces and also in finite electrical networks where the conductance  is symmetric in the vertices  and . We discuss here some situations where the discrete Poisson equation has a solution in infinite networks or in infinite trees, without assuming the symmetry of the conductance.
Keywords: Bipotential infinite networks, Singular vertices in infinite trees, discrete Poisson equation

[1]  Victor Anandam, Harmonic functions and potentials on finite or infinite networks, Springer-Verlag Lecture Notes of the Unione Matematica Italiana 12, 2011.

[3]  I. Bajunaid, J.M. Cohen, F. Colonna and D. Singman, Trees as Brelot Spaces, Adv. in Appl. Math.,30(2003); 706-745.

[3]  I. Bajunaid, J.M. Cohen, F. Colonna and D. Singman, Corrigendum to Trees as Brelot Spaces, Adv. in Appl. Math., (2010); doi:10.1016/j.aam.2010.09.004

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[8]  Sujith Sivan, Madhu Venkataraman, Parahyperbolic Networks,
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[8]  Sujith Sivan, -Potentials in an infinite network, Arab Journal of Mathematical Sciences, 17(2011);101-113.

Abstract:In this paper, we derived some results like the join of two complete Intuitionistic Fuzzy Graphs (IFG) is complete and which is isomorphic to the join of their complements. The nature of edge set in the complement of a complete IFG is analyzed. We study about the join of two IFGs when they are regular, irregular or complete and discuss some theorems. Also we discuss some more properties of the join of two intuitionistic fuzzy graphs using the regularity and irregularity. The minimum and maximum degrees of an IFG and its complement are examined.
Keywords: Intuitionistic Fuzzy Graph (IFG), degree, total degree, Complete IFG, regular IFG, irregular IFG, neighbourly irregular IFG, highly irregular IFGComplement, Join of two IFG.

[1]   K. T. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications. Physica – Verlag, New York, 1999.
[2]   J. George Klir and Bo Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications,  Prentice Hall of India, New Delhi, 2001.
[3]   H. J. Zimmermann, Fuzzy Set Theory and its Applications, Kluwer – Nijhoff, Boston, 1985.
[4]   M. G. Karunambigai and R.Parvathi, Intuitionistic Fuzzy Graphs, Journal of Computational Intelligence: Theory and Applications, 20, 2006, pp. 139 – 150.
[5]   M. S. Sunitha and A. Vijayakumar, Complement of a Fuzzy Graph, Indian Journal of Pure and Applied Mathematics, 33(9), 2002, pp. 1451 – 1464.
[6]    R.Parvathi,  M. G. Karunambigai and K. T. Atanassov, Operations on Intuitionistic Fuzzy Graphs, FUZZ – IEEE, 2009, pp. 1396 – 1401.
[7]    A. Nagoor Gani, R. Jahir Hussain and S. Yahya Mohamed, Irregular Intuitionistic Fuzzy Graph, IOSR Journal MathematicsVol. 9, Issue 6, Jan. 2014, pp. 47 – 51.
[8]   R. Jahir Hussain and S. Yahya Mohamed, More on Irregular Intuitionistic Fuzzy Graphs and its Complements, Discovery Publication, Vol. 21, July 2014, pp. 101 – 107.
[9]   F. Harary, Graph Theor, Addition Wesley, Third Printing, October 1972.
[10]   K. R. Bhutani, Automorphism of Fuzzy Graphs, Pattern Recognition Letter 9: 1989, 159 – 162.