Zagreb indices of block-edge transformation graphs and their complements

Bommanahal Basavanagoud, Shreekant Patil

Abstract


In this paper, we obtain expressions for first and second Zagreb indices and coindices of block-edge transformation graphs G^{ab}. Analogous expressions are obtained also for the complements of G^{ab}.


Keywords


Zagreb index, Zagreb coindex, reformulated Zagreb index, reformulated Zagreb coindex, block-edge transformation graphs G^{ab}

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DOI: http://dx.doi.org/10.19184/ijc.2017.1.2.3

References

A. R. Ashrafi, T. Doslic, A. Hamzeh, The Zagreb coindices of graph operations, Discr. Appl. Math. 158 (2010) 1571--1578.

B. Basavanagoud, S. Patil, Multiplicative Zagreb indices and coindices of some derived graphs, Opuscula Math. 36 (3)(2016) 287--299.

B. Basavanagoud, S. Patil, On the block-edge transformation graphs $G^{ab}$, International Research Journal of Pure Algebra 5 (5) (2015) 75--80.

B. Basavanagoud, I. Gutman, V. R. Desai, Zagreb indices of generalized transformation graphs and their complements, Kragujevac J. Sci. 37 (2015) 99--112.

B. Basavanagoud, I. Gutman, C. S. Gali, On second Zagreb index and coindex of some derived graphs, Kragujevac J. Sci. 37 (2015) 113--121.

G. Chartrand, H. Hevia, E. B. Jarette, M. Schultz, Subgraph distance in graphs defined by edge transfers, Discrete Math. 170 (1997) 63--79.

K. C. Das, I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 52 (2004) 103--112.

T. Doslic, Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008) 66--80.

T. Doslic, B. Furtula, A. Graovac, I. Gutman, S. Moradi, Z. Yarahmadi, On vertex-degree-based molecular structure descriptors, MATCH Commun. Math. Comput. Chem. 66 (2011) 613--626.

B. Furtula, I. Gutman, M. Dehmer, On structure-sensitivity of degree-based topological indices, Appl. Math. Comput. 219 (2013) 8973--8978.

B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015) 1184--1190.

I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (2013) 351--361.

I. Gutman, On the origin of two degree-based topological indices, Bull. Acad. Serbe Sci. Arts (Cl. Sci. Math. Natur.) 146 (2014) 39--52.

I. Gutman, B. Furtula, Z. Kovijanic Vukicevic, G. Popivoda, Zagreb indices and coindices, MATCH Commun. Math. Comput. Chem. 74 (2015) 5--16.

I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004) 83--92.

I. Gutman, Z. Tomovic, On the application of line graphs in quantitative structure-property studies, J. Serb. Chem. Soc. 65 (2000) 577--580.

I. Gutman, Z. Tomovic, More on the line graph model for predicting physico-chemical properties of alkanes, ACH - Models Chem. 137 (2000) 439--445.

I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. Total Pi-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535--538.

I. Gutman, Z. Tomovic, B. K. Mishra, M. Kuanar, On the use of iterated line graphs in quantitative structure-property studies, Indian J. Chem. 40A (2001) 4--11.

F. Harary, Graph Theory, Addison-Wesley, Reading, Mass 1969.

S. M. Hosamani, I. Gutman, Zagreb indices of transformation graphs and total transformation graphs, Appl. Math. Comput. 247 (2014) 1156--1160.

S. M. Hosamani, N. Trinajstic, On reformulated Zagreb coindices, Research Gate 2015-05-08 T 09:07:00 UTC.

A. Milicevic, S. Nikolic, N. Trinajstic, On reformulated Zagreb indices, Mol. Divers. 8 (2004) 393--399.

S. Nikolic, G. Kovacevic, A. Milicevic, N. Trinajstic, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003) 113--124.

J. Senbagamalar, J. Baskar Babujee, I. Gutman, On Wiener index of graph complements, Trans. Comb. 3 (2) (2014) 11--15.

G. Su, L. Xiong, L. Xu, The Nordhaus-Gaddum-type inequalities for the Zagreb index and coindex of graphs, Appl. Math. Lett. 25 (2012) 1701--1707.

Z. Tomovic, I. Gutman, Modeling boiling points of cycloalkanes by means of iterated line graph sequences, J. Chem. Inf. Comput. Sci. 41 (2001) 1041--1045.


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