ON THE SIGMA INDEX OF THE CORONA PRODUCTS OF MONOGENIC SEMIGROUP GRAPHS

Abstract

Keywords

• Monogenic semigroup,Zero-divisor graph,graph products,corona product,graph parameters

References

1. D.F. Anderson and P.S. Livingston, The zero-divisor graph of commutative ring, Journal of Algebra, Vol. 217, pp. 434-447 (1999).
2. D.F. Anderson and A. Badawi, On the zero-divisor graph of a ring, Comm. Algebra, Vol.36(8), pp. 3073-3092 (2008).
3. D.D. Anderson and M. Naseer, Beck's coloring of a commutative ring, Journal of Algebra, Vol.159, pp. 500-514 (1991).
4. I. Beck, Coloring of commutating ring, Journal of Algebra, Vol. 116, pp. 208-226 (1988).
5. F.R. DeMeyer, T. McKenzie and K. Schneider, The zero-divisor graph of a commutative semigroup, Semigroup Forum, Vol. 65, pp. 206-214 (2002).
6. F.R. DeMeyer and L. DeMeyer, Zero-divisor graphs of semigroups, Journal of Algebra, Vol.283, pp. 190-198 (2005).
7. R. Frucht and F. Harary, On the corona of two graphs, Aequationes Math., Vol. 4, pp. 322-325(1970).
8. K.C. Das, N. Akgunes, A.S. Cevik, AS, On a graph of monogenic semigroup. J. Inequal. Appl.2013, 44 (2013).

9. N. Akgunes, Some graph parameters on the strong product of monogenic semigroup graphs,J. Baun Inst. Sci. Technol., XX(X), pp. 1-9 (2018).
10. Y.Nacaroglu, On the corona product of monogenic semigroup graphs, Adv. and Appl. in Discrete Math., in press (2018)
11. J.L. Gross and J. Yellen, Handbook of graph theory, Chapman Hall, CRC Press (2004).
12. W. Imrich and S. Klavzar, Product graphs. structure and recognition, Wiley-Interscience Series in Discrete Math.and Optim., Wiley- Interscience, New York, 2000).
13. S. Klavzar, Coloring graph products - a survey, Discrete Math., Vol. 155, pp. 135-145 (1996).
14. Y. Nacaroglu and A.D. Maden, The Upper Bounds for Multiplicative Sum Zagreb Index of Some Graph Operations, J. of Math. Ineq., Vol. 11(3), pp. 749-761 (2017).
15. Y. Nacaroglu and A.D. Maden, The Multiplicative Zagreb Coindices of Graph Operations, Util. Math., Vol. 102, pp. 19-38 (2017).
16. M. O. Albertson, The irregularity of a graph, Ars Combin., 46, pp. 219{225 (1997).
17. B. Furtula and I. Gutman. A forgotten topological index. J. Math. Chem., Vol. 53(4), pp. 1184-1190 (2015).
18. H. Abdo, D. Dimitrov, The total irregularity of graphs under graph operations, Miskolc Math. Notes 15, pp. 3{17 (2014).
19. I. Gutman, M. Togan, A. Yurttas, A.S. Cevik, I.N. Cangul, Inverse Problem for Sigma Index, MATCH Commun. Math. Comput. Chem., 79, pp. 491-508 (2018).