On Zagreb Indices of Two New Operations of Graphs
Keywords:Degree of vertex, Zagreb indices, Operations of graphs
Recently, Wang et al. (2017) introduced two new operations of graphs. In this paper we establish explicit expressions of some Zagreb indices viz. first Zagreb index, second Zagreb index and forgotten topological index of these two newly proposed operations of graphs. Then as an application we further establish explicit formulae of some other topological indices of the two operations of graphs.
N. De, Sk. Md. A. Nayeem and A. Pal, F-index of some graph operations, Discr. Algo. & Appl. 8(2) (2016), 1650025, DOI: 10.1142/S1793830916500257.
N. De, Sk. Md. A. Nayeem and A. Pal, The F-coindex of some graph operations, SpringerPlus 5 (2016), 221, DOI: 10.1186/s40064-016-1864-7.
H. Deng, D. Saralab, S. K. Ayyaswamy and S. Balachandran, The Zagreb indices of four operations on graphs, Applied Mathematics and Computation 275 (2016), 422 – 431, DOI: 10.1016/j.amc.2015.11.058.
M. V. Diudea and I. Gutman, Wiener-Type topological indices, Croat. Chem. Acta 71 (1) (1998), 21 – 51, https://hrcak.srce.hr/132323.
T. DÅslić, Vertex-weighted Wiener polynomials for composite graphs, Ars Mathematica Contemporanea 1(1) (2008), 66 – 80, DOI: 10.26493/1855-3974.15.895.
C. M. Da Fonseca and D. Stevanovic, Further properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem. 72 (2014), 655 – 668, http://match.pmf.kg.ac.rs/electronic_versions/Match72/n3/match72n3_655-668.pdf.
B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53(4) (2015), 1184 – 1190, DOI: 10.1007/s10910-015-0480-z.
B. Furtula, I. Gutman and S. Ediz, On difference of Zagreb indices, Discrete Applied Mathematics 178 (2014), 83 – 88, DOI: 10.1016/j.dam.2014.06.011.
I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86(4) (2013), 351 – 361, DOI: 10.5562/cca2294.
I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83 – 92, http://match.pmf.kg.ac.rs/electronic_versions/Match50/match50_83-92.pdf.
I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total (pi)-electron energy of alternate hydrocarbons, Chem. Phys. Lett. 17(4) (1972), 535 – 538, DOI: 10.1016/0009-2614(72)85099-1.
I. Gutman, B. Furtula, Ž. K. Vukićević and G. Popivoda, On Zagreb indices and coindices, MATCH Commun. Math. Comput. Chem. 74 (2015), 5 – 16, http://match.pmf.kg.ac.rs/electronic_versions/Match74/n1/match74n1_5-16.pdf.
R. Hammack, W. Imrich and S. Klavžar, Handbook of Products Graphs, 2nd edition, CRC Press, Boca Raton (2011), DOI: 10.1201/b10959.
M. H. Khalifeh, H. Yousefi-Azari and A. R. Ashrafi, The first and second Zagreb indices of some graph operations, Discr. Appl. Math. 157(4) (2009), 804 – 811, DOI: 10.1016/j.dam.2008.06.015.
G. H. Shirdel, H. Rezapour and A. M. Sayadi, The hyper-Zagreb index of graph operations, Iranian J. Math. Chem. 4 (2013), 213 – 220, DOI: 10.22052/ijmc.2013.5294
D. Wang, Y. Hou and Z. Tang, The adjacency spectrum of two new operations of graphs, AKCE International Journal of Graphs and Combinatorics 15(3) (2018), 284 – 290, DOI: 10.1016/j.akcej.2017.10.004.
D. B. West, Introduction to Graph Theory, Pearson Education Pte. Ltd., Singapore (2002).
B. Zhou and I. Gutman, Further properties of Zagreb indices, MATCH Commun. Math. Comput. Chem. 54 (2005), 233 – 239, http://match.pmf.kg.ac.rs/electronic_versions/Match54/n1/match54n1_233-239.pdf
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