Vertex and edge Co-PI indices of bridge graphs

  • Authors

    • Sharmila Devi Kongu Arts and Science College (Autonomous), Erode.
    • V. Kaladevi Bishop Heber College, Trichy
    2016-02-13
    https://doi.org/10.14419/ijams.v6i1.8398
  • Bridge Graph, Co-PI Index, Edge Co-PI Index.

  • Abstract

    The Co-PI index of a graph G is denoted by Co-PI(G) and  is defined as Co-PI(G  is the number of vertices of G whose distance to the vertex u is less than the distance to the vertex v in G. Similarly, the edge Co-PI index of G is defined as Co-PIe(G) is number of edges of G whose distance  to the vertex u is less than the distance to the vertex v in G.  In this paper, the upper bounds for the Co-PI and edge Co-PI indices of bridge graph are obtained.

  • References

    1. [1] Ashrafi A.R., Loghman A., PI index of zig-zag polyhex nanotubes, MATCH Commun. Math. Comput. Chem. 55(2006) 447-452.

      [2] Ashrafi A.R., Rezaei F., PI index of polyhex nanotori, MATCH Commun. Math. Comput. Chem. 57(2007) 243-250.

      [3] Ashrafi A.R., Loghman A., PI index of armchair polyhex nanotubes, Ars Combin. 80(2006) 193-199.

      [4] Barriere L., Comellas F., Dalfo C and Fiol M A., The hierarchical product of graphs, Discrete Appl. Math. 157(2009) 36-48.

      [5] Barriere L., Dalfo C., Fiol M A., and Mitjana., The generalized hierarehical product of graphs, Discrete Math. 309(2009) 3871-3881.

      [6] Deng H., Chen S., Zhang J., The PI index of phenylenes, J. Math. Chem. 41(2007) 63-69.

      [7] Eliasi M., Iranmanesh A., The hyper-Wiener index of the generalized hierarchical product of graphs, Discrete Appl. Math. 159(2011) 866-871.

      [8] Hoji M., Luo Z., Vumar E., Wiener and vertex PI indices of Kronecker products of graphs, Discrete Appl. Math. 158 (2010) 1848-1855.

      [9] Khalifeh M H., Yousefi Azari H and Ashrafi A R., Vertex and edge PI indices of cartesian product graphs, Discrete Appl. Math. 156(2008) 1780-1789.

      [10] Khadikar P.V., On a novel structural descriptor PI, Nat. Acad. Sci. Lett. 23(2000) 113-118.

      [11] Khalifeh M.H., Yousefi-Azari H., Ashrafi A.R., The hyper-Wiener index of graph operations, Comput. Math. Appl. 56(2008) 1402 - 1407.

      [12] Khadikar P.V., Karmarkar S., Agrawal V.K., A novel PI index and its application to QSPR/QSAR studies, J. Chem. Inf. Comput. Sci. 41(2001) 934-949.

      [13] Klavˇzar S., On the PI index: PI-partitions and Cartesian product graphs, MATCH Commun. Math. Comput. Chem. 57(2007) 573-586.

      [14] Pattabiraman K., Paulraja P., On some topological indices of the tensor products of graphs, Discrete Appl. Math. 160(2012) 267-279.

      [15] Pattabiraman K.,Paulraja P.,Vertex and edge padmakar Ivan indices of generalized hierarchical product of graphs, Discrete Appl.

      Math.160(2012),13761384.

      [16] Pattabiraman K., Paulraja P., Wiener and vertex PI indices of the strong product of graphs, Discuss. Math. Graph Theory 32(2012) 749-769.

      [17] Yousefi-Azari H., Manoochehrian B., Ashrafi A.R., The PI index of product graphs, Appl. Math. Lett. 21(2008) 624-627.

      [18] Wiener H., Structural determination of the paraffin boiling points, J. Am. Chem. Soc. 69(1947) 17-20.

      [19] Ilic A and Milosavljevic N., The weighted vertex PI index, Math. Comput. Model. 57 623-631.

      [20] Mansour T., Schork M., The PI index of bridge and chain graphs, MATCH Commun. Math. Comput. Chem. 61:3(2009) 723-734.

      [21] Mansour T., Schork M., The vertex PI index and Szeged index of bridge graphs, Discrete Appl. Math. 157(2009) 1600-1606.

      [22] Mansour T., Schork M., The PI Index of Polyomino Chains of 4k-Cycles, Acta Appl. Math. 109(2010) 671-681.

  • Downloads

  • How to Cite

    Devi, S., & Kaladevi, V. (2016). Vertex and edge Co-PI indices of bridge graphs. International Journal of Advanced Mathematical Sciences, 4(2), 44-46. https://doi.org/10.14419/ijams.v6i1.8398