IJPAM: Volume 106, No. 4 (2016)


Gee-Choon Lau$^1$, Hong-Heng Chu$^2$, Nurulzulaiha Suhadak$^3$,
Fong-Yeng Foo$^4$, Ho-Kuen Ng$^5$
$^{1,2,3,4}$Faculty of Computer & Mathematical Sciences
Universiti Teknologi MARA (Segamat Campus)
85000, Johor, MALAYSIA
$^5$Department of Mathematics
San Jose State University
San Jose, CA 95192, USA

Abstract. Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. Given a bijection $f: V(G) \to \{1, \ldots, n\}$, we associate 2 integers $S = f(u) + f(v)$ and $D = \vert f(u) - f(v)\vert$ with every edge $uv$ in $E(G)$. The labeling $f$ induces an edge labeling $f':E(G) \to \{0, 1\}$ such that for any edge $uv$ in $E(G)$, $f'(uv) = 1$ if $gcd(S,D) = 1$, and $f'(uv) = 0$ otherwise. Let $e_{f'}(i)$ be the number of edges labeled with $i\in\{0,1\}$. We say $f$ is an SD-prime cordial labeling if $\vert e_{f'}(0) - e_{f'}(1)\vert \le 1$. Moreover $G$ is SD-prime cordial if it admits an SD-prime cordial labeling. In this paper, we investigate the SD-prime cordiality of some standard graphs.

Received: November 22, 2015

AMS Subject Classification: 05C78, 05C25

Key Words and Phrases: prime labeling, prime cordial labeling, SD-prime labeling, SD-prime cordial labeling

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DOI: 10.12732/ijpam.v106i4.4 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: 106
Issue: 4
Pages: 1017 - 1028

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