Geodesic
The Product Connectivity Banhatti Index of a Graph
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 505-517.

Voir la notice de l'article provenant de la source Library of Science

Let G = (V, E) be a connected graph with vertex set V (G) and edge set E(G). The product connectivity Banhatti index of a graph G is defined as, PB(G)= ∑_ue1√( d_G(u) d_G(e) ), where ue means that the vertex u and edge e are incident in G. In this paper, we determine PB(G) of some standard classes of graphs. We also provide some relationship between PB(G) in terms of order, size, minimum / maximum degrees and minimal non-pendant vertex degree. In addition, we obtain some bounds on PB(G) in terms of Randić, Zagreb and other degree based topological indices of G.
Keywords: Randić index, Zagreb indices, Banhatti indices, product connectivity Banhatti index 
@article{DMGT_2019_39_2_a13,
     author = {Kulli, V.R. and Chaluvaraju, B. and Boregowda, H.S.},
     title = {The {Product} {Connectivity} {Banhatti} {Index} of a {Graph}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {505--517},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a13/}
}
TY  - JOUR
AU  - Kulli, V.R.
AU  - Chaluvaraju, B.
AU  - Boregowda, H.S.
TI  - The Product Connectivity Banhatti Index of a Graph
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2019
SP  - 505
EP  - 517
VL  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a13/
LA  - en
ID  - DMGT_2019_39_2_a13
ER  - 
%0 Journal Article
%A Kulli, V.R.
%A Chaluvaraju, B.
%A Boregowda, H.S.
%T The Product Connectivity Banhatti Index of a Graph
%J Discussiones Mathematicae. Graph Theory
%D 2019
%P 505-517
%V 39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a13/
%G en
%F DMGT_2019_39_2_a13
Kulli, V.R.; Chaluvaraju, B.; Boregowda, H.S. The Product Connectivity Banhatti Index of a Graph. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 505-517. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a13/

[1] K.Ch. Das, S. Das and B. Zhou, Sum-connectivity index of a graph, Front. Math., China 11 (2016) 47–54. doi:10.1007/s11464-015-0470-2

[2] I. Gutman and B. Furtula, Recent Results in the Theory of Randić Index (Univ. Kragujevac, Kragujevac, 2008).

[3] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total ϕ-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538. doi:10.1016/0009-2614(72)85099-1

[4] I. Gutman, V.R. Kulli, B. Chaluvaraju and H.S. Boregowda, On Banhatti and Zagreb indices, J. Int. Math. Virtual Inst. 7 (2017) 53–67. doi:10.7251/JIMVI1701053G

[5] V.R. Kulli, College Graph Theory (Vishwa International Publications, Gulbarga, India, 2012).

[6] V.R. Kulli, On K Banhatti indices of graphs, J. Comput. Math. Sci. 7 (2016) 213–218.

[7] V.R. Kulli, On K indices of graphs, Internat. J. Fuzzy Math. Arch. 10 (2016) 105–109.

[8] V.R. Kulli, The first and second Ka indices and coindices of graphs, Internat. J. Math. Arch. 7 (2016) 71–77.

[9] V.R. Kulli, B. Chaluvaraju and H.S. Boregowda, On sum-connectivity Banhatti index of some nanostructures, submitted.

[10] X. Li and I. Gutman, Mathematical aspects of Randić-type molecular structure descriptors, Math. Chem. Monogr. 1 (Univ. Kragujevac, Kragujevac, 2006).

[11] M. Randić, On characterization of molecular branching, J. Amer. Chem. Soc. 97 (1975) 6609–6615. doi:10.1021/ja00856a001

[12] T. Mansour, M.A. Rostami, E. Suresh and G.B.A. Xavier, On the bounds of the first reformulated Zagreb index, Turkish J. Anal. Number Theory 4 (2016) 8–15. doi:10.12691/tjant-4-1-2

[13] S. Nikolić, G. Kovačević, A. Miličević and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003) 113–124.

[14] B. Zhou and N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46 (2009) 1252–1270. doi:10.1007/s10910-008-9515-z

[15] B. Zhou and N. Trinajstić, On general sum-connectivity index, J. Math. Chem. 47 (2010) 210–218. doi:10.1007/s10910-009-9542-4