SCHULTZ POLYNOMIALS AND THEIR TOPOLOGICAL INDICES OF SUSPENSION GRAPHS

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Published: Nov 13, 2017

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BHAGYASHRI R DODDAMANI
KARNATAK UNIVERSITY
Dr. Keerthi G. Mirajkar
Karnatak University

Abstract

Let G = (V, E) be a simple connected graph. The degree of a
vertex u and the distance between the vertices u and v are denoted
by du and d(u; v) of a graph G respectively. The Schultz and modied
Schultz polynomials are Sc(G, x) = ∑ (u,v) ε V(G)(du + dv) Xd(u, v) and

Sc*(G, x) =∑ (u,v) ε V(G)(du dv) Xd(u, v) respectively. Then their first
derivative at x = 1 are equal to Sc(G) = ∑ (u,v) ε V(G)(du + dv) d(u, v)
and Sc*(G) = ∑ (u,v) ε V(G)(du dv) d(u, v) are known as Schultz index
and modified Schultz index respectively. In this paper, we compute
the Schultz and modified Schultz polynomials and their indices for the
suspension graphs K1+Kn Ɐ n ε N, K1+Kn, n Ɐ n ε N, K1+Kn, m  Ɐ n, m ε N, n ≠ m 

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How to Cite
DODDAMANI, B. R., & Mirajkar, D. K. G. (2017). SCHULTZ POLYNOMIALS AND THEIR TOPOLOGICAL INDICES OF SUSPENSION GRAPHS. Journal of Global Research in Mathematical Archives(JGRMA), 4(11), 21–29. Retrieved from https://jgrma.com/index.php/jgrma/article/view/340
Issue
Vol. 4 No. 11 (2017): November-2017
Section
Research Paper
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Author Biographies

BHAGYASHRI R DODDAMANI, KARNATAK UNIVERSITY

Department of Mathematics

Dr. Keerthi G. Mirajkar, Karnatak University

Department of Mathematics

References

A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees;Theory

and applications, Acta. Appl. Math., 66, (2001), 211-249.

M. Eliasi and B. Taeri, Shultz polynomials of composite graphs, Appli-

cable Analysis and Discrete Mathematics, 2, (2008), 285-296.

M. R. Farahani, Shultz, Modied schultz polynomial, Hosoya polyno-

mial and wiener index of circumcoronene series of Bezenoid, Applied

mathematics and information sciences, 31(5-6), (2013), 595-608.

M. R. Farahani, Schultz indices and schultz polynomials of Harary

graph, Pacific Journal of Applied Mathematics, 6(3), (2014), 77-84.

M. R. Farhani, W. Gao and M. R. Rajesh Kanna, The schultz, modified

schultz indices and their polynomials of the jahangir graphs Jn;m for

integer numbers n=3, m > 3, Asian journal of applied sciences, 3(6),

(2015), 823-827.

M. R. Farahani and Hosoya, Schultz, Modified schultz polynomials and

their topological indices of benzene molecules: First members of poly-

cyclic Aromatic hydrocarbons[PAHs], International journal of theoroti-

cal chemistry, 1(2), (2013), 9-16.

I. Gutman, Some Relations between Distance-based polynomials of

trees, Sciences Mathematiques, 30, (2005), 1-7.

I. Gutman, S. Klavzar, Wiener number of vertex-weighted graphs and a chemical application, Disc. Appl. Math., 80, (1997), 73-81.

I. Gutman, O. E. Polansky, Mathematical concepts in organic chemistry, Springer, Berlin, 1986.

F. Hassani, A. Iranmanesh, S. Mirzaie, Schultz and modified schultz

polynomials of C100 fullerence, MATCH Commun. Math. Comput.

Chem., 69, (2013), 87-92.

H. Hosoya, On some counting polynomials in chemistry, Discrete Applied Mathematics, 19, (1988), 239-257.

H. P. Schultz, Topological organic chemistry 1. Graph theory and topological indices of alkanes, J. Chem. Inf. Comput. Sci., 29, (1989), 227-228.

H. Wiener, Structural determination of paran boiling points, J. Amer. Chem. Soc., 69, (1947), 17-20.

Z. Yarahmadi, T. Doslic and A. R. Ashra, The bipartite edge frustra

tion of composite graphs, Disc. Appl. Math., 158, (2010), 1551-1558.