IJPAM: Volume 110, No. 4 (2016)

Title

POLYNOMIAL FAMILY GRAPH OF $\mathbb{Z}_n$

Authors

J. John Arul Singh$^1$, S. Devi$^2$
$^{1,2}$Department of Mathematics
Noorul Islam Centre for Higher Education
Thuckalay, 629 180, Kanyakumari, Tamilnadu, INDIA

Abstract

The polynomial family graph $\Gamma_\mathscr{P} (R)$ of a finite ring R generated by a family of polynomials $\mathscr{P}\subseteq R[x]$ is a graph in which the elements of the ring are the vertices and two distinct elements $a$ and $b$ are adjacent if $p(a)=b$ for some $p(x)\in\mathscr{P}$. In this paper $\Gamma_\mathscr{P} (\mathbb Z_n)$ generated by the polynomial family $\mathscr{P}=\{ax+b~:~a,b\in\{1,~-1\} \}$ is studied and bounds for some domination parameters are given.

History

Received: July 1, 2016
Revised: October 9, 2016
Published: November 9, 2016

AMS Classification, Key Words

AMS Subject Classification: 05C
Key Words and Phrases: polynomial family graph, domination, chromatic, independence

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Bibliography

1
Frank Hahary, Graph Theory, Addison-Wesley Publishing Company, Massachusetts Menlo Park, California London Don Mills, 1969.

2
I.N. Herstein, Topics in Algebra, John Wiley and Sons, New York-Chichester-Brisbane-Toronto-Singapore, 1975.

How to Cite?

DOI: 10.12732/ijpam.v110i4.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 110
Issue: 4
Pages: 581 - 585


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