IJPAM: Volume 110, No. 4 (2016)




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


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.


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

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.


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

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?

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

$\mathbb{Z}_n$%22&as_occt=any&as_epq=&as_oq=&as_eq=&as_publication=&as_ylo=&as_yhi=&as_sdtAAP=1&as_sdtp=1" title="Click to search Google Scholar for this entry" rel="nofollow">Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).