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Year 2019, Volume 9, Issue 4, 747 - 754, 01.12.2019

Abstract

References

  • [1] Adiga, C. and Malpashree, R., (2016), The degree status connectivity index of graphs and its multiplicative version, South Asian J. of Math., 6(6), pp. 288 - 299.
  • [2] Ashrafi, A.R. and Ghorbani, M., (2010), Eccentric connectivity index of fullerenes In: I. Gutman, B. Furtula,(eds.) Novel Molecular Structure Descriptors - Theory and Applications II, Uni. Kragujevac, Kragujevac, pp. 183 - 192.
  • [3] Ashrafi, A.R., Saheli, M. and Ghorbani, M., (2011), The eccentric connectivity index of nanotubes and nanotori, J. Comput. Appl. Math., 235, pp. 4561 - 4566.
  • [4] Balaban, A.T., (1976), Chemical Applications of Graph Theory, Academic Press, London.
  • [5] Das, K.C., Xu, K. and Nam, J., (2015), Zagreb indices of graphs, Front. Math. China, 10, pp. 567 - 582.
  • [6] Das, K.C., Lee, D. and Graovac, A., (2013), Some properties of the Zagreb eccentricity indices, Ars Math. Contemp., 6, pp. 117 - 125.
  • [7] Devillers, J. and Balaban, A.T., (1999), Topological indices and related descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, The Netherlands.
  • [8] Furtula, B., Gutman, I. and Dehmer, M., (2013), On structure sensitivity of degree based topological indices, Appl. Math. Comput., 219, pp. 8973 - 8978.
  • [9] Graovac, A., Gutman, I. and Vukiˇcevi´c, D. (Ed.), (2009), Mathematical Methods and Modelling for Students of Chemistry and Biology, Hum Press, Zagreb.
  • [10] Gutman, I. and Trinajstic, N., (1972), Graph theory and molecular orbitals, Total Π electron energy of alternate hydrocarbons, Chem. Phy. Letters, 17, pp. 535 - 538.
  • [11] Gutman, I., (2003), Introduction to Chemical Graph Theory, Fac. Sci. Kragujevac, Kragujevac (in Serbian).
  • [12] Gutman, I.(Ed.), (2006), Mathematical Methods in Chemistry, Prijepolje Museum, Prijepolje.
  • [13] Gutman, I. and Das, K.C., (2004), The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50, pp. 83 - 92.
  • [14] Gutman, I., (2013), Degree based topological indices, Croat. Chem. Acta, 86, pp. 351 - 361.
  • [15] Gutman, I. and Furtula, B., (2015), Metric extremal graphs in: Dehmer, M. and Emmert-Streib. F. (Eds.), Quantitative Graph Theory Mathematical Foundations and Applications, CRC Press, Boca Raton, pp. 111 - 139.
  • [16] Harary, F., (1959), Status and contrastatus, Sociometry, 22, pp. 23 - 43.
  • [17] Illi´c, A. and Milosavljevi´c, N., (2013), The Weighted vertex PI index, Math. Comput. Model, 57, pp. 623 - 631.
  • [18] Illi´c, A. and Gutman, I., (2011), Eccentric connectivity index of chemical trees, MATCH Commun. Math. Comput. Chem., 65, pp. 731 - 744.
  • [19] Khalifeh, M.H., Yousefi-Azari, H. and Ashrafi, A.R., (2009), The first and second Zagreb indices of some graph operations, Discrete Appl. Math., 157, pp. 804 - 8
  • [20] Klavˇzar, S., (2007), On the PI index: PI-partitions and Cartesian product graphs, MATCH Commun. Math. Comput. Chem., 57, pp. 573-586.
  • [21] Nilanjan, De., Abu Nayeem, Sk. Md. and Anita, P., (2016), The F-coindex of some graph operations, Springer Plus, 5 (221), 13 pages.
  • [22] Pattabiraman, K. and Kandan, P., (2016), On weighted PI index of graphs, Elect. Notes in Discrete Math., 53, pp. 225 - 238.
  • [23] Pattabiraman, K. and Kandan, P., (2015), Generalization on degree distance of tensor product of graphs, Aust. J. Combin., 62, pp. 211 - 227.
  • [24] Pattabiraman, K. and Kandan, P., (2015), Generalization on degree distance of strong product of graphs, Iranian J. Math. Sci.& informatics, 10(2), pp. 87 - 98.
  • [25] Pattabiraman, K. and Kandan, P., (2014), Weighted PI index of corona product of graphs, Discrete Math. Alg. Appl., 6(4), 1450055 (9 pages).
  • [26] Pattabiraman, K. and Paulraja, P., (2012), Wiener and vertex Padmakar-Ivan indices of the strong product of graphs, Discuss. Math. Graph Theory, 32, pp. 749 - 769.
  • [27] Ramane, H. S. and Yalnaik, A.S., (2017), Status connectivity indices of graphs and its applications to the boiling point of benzenoid hydrocarbons, J. Appl. Math. Comput., 55(1-2), pp. 609 - 627.
  • [28] Ramane, H.S., Yalnaik, A.S. and Sharafdini, R., (2018), Status connectivity indices and co-indices of graphs and its computation to some distance-balanced graph, AKCE Int. J. of Graphs and Comb., In Press.
  • [29] Sheeba Agnes, V., (2014), Degree distance of tensor product and strong product of graphs, Filomat, 28(10), pp. 2185 - 2198.
  • [30] Todeschini, R. and Consonni, V., (2009), Molecular Descriptors for Chemoinformatics, Wiley VCH, Weinheim.
  • [31] Wiener, H., (1947), Structural determination of paraffin boiling points., J. Am. Chem. Soc., 69, pp. 17 - 20.
  • [32] Xu, K., Liu, M., Das, K. C., Gutman, I. and Furtula, B., (2014), A survey on graphs extremal with respect to distance based topological indices, MATCH Commun. Math. Comput. Chem., 71, pp. 461 - 508.
  • [33] Yarahmadi, Z. and Ashrafi, A. R., (2012), The Szeged, vertex PI, first and second Zagreb indices of corona product of graphs, Filomat, 26, pp. 467 - 472.

STATUS CONNECTIVITY INDICES OF CARTESIAN PRODUCT OF GRAPHS

Year 2019, Volume 9, Issue 4, 747 - 754, 01.12.2019

Abstract

In this paper, we establish one of the recent topological indices called the first status connectivity index S1 G = P uv2E G [G u + G v ] and second status connectivity index S2 G = P uv2E G [G u G v ] of Cartesian product of two simple graphs are determined. Also these indices are computed for nanotube, nanotorus, grid and cartesian product of complete graphs.

References

  • [1] Adiga, C. and Malpashree, R., (2016), The degree status connectivity index of graphs and its multiplicative version, South Asian J. of Math., 6(6), pp. 288 - 299.
  • [2] Ashrafi, A.R. and Ghorbani, M., (2010), Eccentric connectivity index of fullerenes In: I. Gutman, B. Furtula,(eds.) Novel Molecular Structure Descriptors - Theory and Applications II, Uni. Kragujevac, Kragujevac, pp. 183 - 192.
  • [3] Ashrafi, A.R., Saheli, M. and Ghorbani, M., (2011), The eccentric connectivity index of nanotubes and nanotori, J. Comput. Appl. Math., 235, pp. 4561 - 4566.
  • [4] Balaban, A.T., (1976), Chemical Applications of Graph Theory, Academic Press, London.
  • [5] Das, K.C., Xu, K. and Nam, J., (2015), Zagreb indices of graphs, Front. Math. China, 10, pp. 567 - 582.
  • [6] Das, K.C., Lee, D. and Graovac, A., (2013), Some properties of the Zagreb eccentricity indices, Ars Math. Contemp., 6, pp. 117 - 125.
  • [7] Devillers, J. and Balaban, A.T., (1999), Topological indices and related descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, The Netherlands.
  • [8] Furtula, B., Gutman, I. and Dehmer, M., (2013), On structure sensitivity of degree based topological indices, Appl. Math. Comput., 219, pp. 8973 - 8978.
  • [9] Graovac, A., Gutman, I. and Vukiˇcevi´c, D. (Ed.), (2009), Mathematical Methods and Modelling for Students of Chemistry and Biology, Hum Press, Zagreb.
  • [10] Gutman, I. and Trinajstic, N., (1972), Graph theory and molecular orbitals, Total Π electron energy of alternate hydrocarbons, Chem. Phy. Letters, 17, pp. 535 - 538.
  • [11] Gutman, I., (2003), Introduction to Chemical Graph Theory, Fac. Sci. Kragujevac, Kragujevac (in Serbian).
  • [12] Gutman, I.(Ed.), (2006), Mathematical Methods in Chemistry, Prijepolje Museum, Prijepolje.
  • [13] Gutman, I. and Das, K.C., (2004), The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50, pp. 83 - 92.
  • [14] Gutman, I., (2013), Degree based topological indices, Croat. Chem. Acta, 86, pp. 351 - 361.
  • [15] Gutman, I. and Furtula, B., (2015), Metric extremal graphs in: Dehmer, M. and Emmert-Streib. F. (Eds.), Quantitative Graph Theory Mathematical Foundations and Applications, CRC Press, Boca Raton, pp. 111 - 139.
  • [16] Harary, F., (1959), Status and contrastatus, Sociometry, 22, pp. 23 - 43.
  • [17] Illi´c, A. and Milosavljevi´c, N., (2013), The Weighted vertex PI index, Math. Comput. Model, 57, pp. 623 - 631.
  • [18] Illi´c, A. and Gutman, I., (2011), Eccentric connectivity index of chemical trees, MATCH Commun. Math. Comput. Chem., 65, pp. 731 - 744.
  • [19] Khalifeh, M.H., Yousefi-Azari, H. and Ashrafi, A.R., (2009), The first and second Zagreb indices of some graph operations, Discrete Appl. Math., 157, pp. 804 - 8
  • [20] Klavˇzar, S., (2007), On the PI index: PI-partitions and Cartesian product graphs, MATCH Commun. Math. Comput. Chem., 57, pp. 573-586.
  • [21] Nilanjan, De., Abu Nayeem, Sk. Md. and Anita, P., (2016), The F-coindex of some graph operations, Springer Plus, 5 (221), 13 pages.
  • [22] Pattabiraman, K. and Kandan, P., (2016), On weighted PI index of graphs, Elect. Notes in Discrete Math., 53, pp. 225 - 238.
  • [23] Pattabiraman, K. and Kandan, P., (2015), Generalization on degree distance of tensor product of graphs, Aust. J. Combin., 62, pp. 211 - 227.
  • [24] Pattabiraman, K. and Kandan, P., (2015), Generalization on degree distance of strong product of graphs, Iranian J. Math. Sci.& informatics, 10(2), pp. 87 - 98.
  • [25] Pattabiraman, K. and Kandan, P., (2014), Weighted PI index of corona product of graphs, Discrete Math. Alg. Appl., 6(4), 1450055 (9 pages).
  • [26] Pattabiraman, K. and Paulraja, P., (2012), Wiener and vertex Padmakar-Ivan indices of the strong product of graphs, Discuss. Math. Graph Theory, 32, pp. 749 - 769.
  • [27] Ramane, H. S. and Yalnaik, A.S., (2017), Status connectivity indices of graphs and its applications to the boiling point of benzenoid hydrocarbons, J. Appl. Math. Comput., 55(1-2), pp. 609 - 627.
  • [28] Ramane, H.S., Yalnaik, A.S. and Sharafdini, R., (2018), Status connectivity indices and co-indices of graphs and its computation to some distance-balanced graph, AKCE Int. J. of Graphs and Comb., In Press.
  • [29] Sheeba Agnes, V., (2014), Degree distance of tensor product and strong product of graphs, Filomat, 28(10), pp. 2185 - 2198.
  • [30] Todeschini, R. and Consonni, V., (2009), Molecular Descriptors for Chemoinformatics, Wiley VCH, Weinheim.
  • [31] Wiener, H., (1947), Structural determination of paraffin boiling points., J. Am. Chem. Soc., 69, pp. 17 - 20.
  • [32] Xu, K., Liu, M., Das, K. C., Gutman, I. and Furtula, B., (2014), A survey on graphs extremal with respect to distance based topological indices, MATCH Commun. Math. Comput. Chem., 71, pp. 461 - 508.
  • [33] Yarahmadi, Z. and Ashrafi, A. R., (2012), The Szeged, vertex PI, first and second Zagreb indices of corona product of graphs, Filomat, 26, pp. 467 - 472.

Details

Primary Language English
Journal Section Research Article
Authors

P. KANDAN This is me
Department of Mathematics,Annamalai University,Annamalainagar 608 002, India.

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760944, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {747 - 754}, title = {STATUS CONNECTIVITY INDICES OF CARTESIAN PRODUCT OF GRAPHS}, key = {cite}, author = {Kandan, P.} }