IJPAM: Volume 90, No. 4 (2014)

DETERMINANT OF ADJACENCY MATRIX
OF SQUARE CYCLE GRAPH

Nitiphoom Adsawatithisakul$^1$, Decha Samana$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
King Mongkut's Institute of Technology Ladkrabang
Bangkok 10520, THAILAND


Abstract. Square Cycle, $C_n^2$ is a graph that has $n$ vertices and two vertices $u$ and $v$ are adjacent if and only if distance between $u$ and $v$ not greater than 2. In this paper, we show that the determinant of adjacency matrix of square cycle $C_n^2$ are as follows

$det(A(C_n^{2}))=\left\{ \begin{array}{ll} 0, & \hbox{$n \equiv 0,2,4 \bmod 6$... ...quiv 3 \bmod 6$} ,\\ 4, & \hbox{$n \equiv 1,5 \bmod 6$}. \end{array} \right.$


Received: May 21, 2013

AMS Subject Classification: 05C50

Key Words and Phrases: determinant, square cycle graph, adjacency matrix

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DOI: 10.12732/ijpam.v90i4.3 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: 2014
Volume: 90
Issue: 4