IJPAM: Volume 105, No. 4 (2015)

THE $\ga$-SPECTRUM OF CYCLE WITH ONE CHORD

Varanoot Khemmani$^1$, Supaporn Saduakdee$^2$
$^1$Department of Mathematics
Srinakharinwirot University
Sukhumvit 23, Bangkok, 10110, THAILAND


Abstract. Let $G$ be a graph of order $n$ and size $m$. A $\ga$-labeling of $G$ is a one-to-one function $f: V(G) \rightarrow \{0, 1, 2, \ldots, m\}$ that induces an edge-labeling $f': E(G) \rightarrow \{1, 2, \ldots, m\}$ on $G$ defined by $f'(e)=\vert f(u)-f(v)\vert$ for each edge $e=uv$ of $G$. The value of $f$ is defined as

\begin{displaymath}{\rm val}(f)=\sum_{e\in E(G)}f'(e)\, . \end{displaymath}

The $\ga$-spectrum of a graph $G$ is defined as $\spec(G) = \{\val(f) : \mbox{$f$\ is a $\ga$-labeling of $G$}\}$.

In this paper, $\ga$-spectrum of cycle with one chord is determined.

Received: October 15, 2015

AMS Subject Classification: 05C78

Key Words and Phrases: $\ga$-labeling, $\ga$-spectrum, cycle with one chord

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DOI: 10.12732/ijpam.v105i4.22 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: 2015
Volume: 105
Issue: 4
Pages: 835 - 852


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