ON ZAGREB COINDEX POLYNOMIALS FOR SOME SPECIAL GRAPHS

Aliyu Ibrahim  Kiri; Aliyu  Suleiman

Aliyu Ibrahim Kiri
Aliyu Suleiman

Keywords: Zagreb Index, Zagreb Polynomial, Complete Graph, Complete bipartite graph, Cycle

Abstract

Zagreb polynomial is a polynomial in which the power of the indeterminate is a Zagreb index, Zagreb index is a graph invariant as it remains fixed under graph homomorphism. The complement of a graph is needed to compute the Zagreb coindex as well as the polynomial. In this paper we looked at the size of the complement graphs under consideration and the formulae for their Zagreb coindex polynomials.The graphs are cycle C_n, wheel W_n, path P_n, complete graph K_n and the complete bipartite graph K_m;n.

References

G. Chartrand, P. Zhang. A First Course in Graph Theory. Dover Publications Inc. Mineola, New York (2012)

J.A. Bondy, U.S.R. Murty. Graph Theory With Applications. 5th Edition. Elsevier Science Publishing Co. Inc. New York (1982)

V.K. Balakrishnan. Theory and Problems of Graph Theory. McGraw-Hill Companies. U.S.A. (1997)

I. Gutman, N. Trinajstic. Graph Theory and molecular orbitals. Total pi- electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17(4): (1972), 535-538.

B. Basavanagoud, V.R. Desal, K.G. Mirajkar, B. Pooja, I.N. Caugul. Four New Tensor Product of graphs and their Zagreb indices and coindices. Electronic Journal of Mathematical Analysis and Applications. 8(1): (2020), 209-219.

D. Rajarethinam, A.Q. Baig, W. Sajjad, M.R. Farahani. Eccentric Connectivity Polynomial and Total Eccentricity Polynomial of NAnm Nanotube. Journal of Informatics and Mathematical Sciences. 9(1): (2017), 201-215.

A. Parvez, S.A. K. Kirmani, O. Al-Rugaie, F. Azam. Degree Based Topological Indices and Polynomials of hyaluronic acid-corcumin Conjugates. Saudi Pharmaceutical Journal. 28(9): (2020), 1093-1100.

H. Wiener. Structural determination of the paraffin boiling points. J. Am. Chem. Soc. 26: (1947), 17-20.

I. Gutman, O.E. Polansky. Mathematical Concept in Organic Chemistry. Springer Science and Business Media. (2012).

F. Harary. Graph Theory. Addison-Wesley. Reading (1969).

H.M.A. Siddiqui. Computation of Zagreb Indices and Zagreb Polynomials of Sierpinski Graphs. Hacette Journal of Mathematics and Statistics. 49(2): (2020), 754-765.

T. Doslic. Vetex-weighted Wiener polynomials for composite graphs. Arts Math. Contemp. 1: (2008), 66-80.

A. R. Ashra , A. Hamzeh, S. Hossein-Zadeh. Caalculation of some Topological Indices of Slices and Links of Graphs. J. Appl. Math. and Informatics. 29(1-2): (2014), 327-333.