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The eigenvalues and energy of integral circulant graphs | ||
| Transactions on Combinatorics | ||
| مقاله 6، دوره 1، شماره 3، آذر 2012، صفحه 47-56 اصل مقاله (486.84 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2012.1909 | ||
| نویسنده | ||
| Mohsen Mollahajiaghaei* | ||
| Amirkabir University | ||
| چکیده | ||
| A graph is called \textit{circulant} if it is a Cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. Let $D$ be a set of positive, proper divisors of the integer $n>1$. The integral circulant graph $ICG_{n}(D)$ has the vertex set $\mathbb{Z}_{n}$ and the edge set E$(ICG_{n}(D))= \{\{a,b\}; gcd(a-b,n)\in D \}$. Let $n=p_{1}p_{2}\cdots p_{k}m$, where $p_{1},p_{2},\cdots,p_{k}$ are distinct prime numbers and $gcd(p_{1}p_{2}\cdots p_{k},m)=1$. The open problem posed in paper [A. Ili'{c}, The energy of unitary Cayley graphs, Linear Algebra Appl., 431 (2009) 1881--1889] about calculating the energy of an arbitrary integral circulant $ICG_{n}(D)$ is completely solved in this paper, where $D=\{p_{1},p_{2},\ldots,p_{k} \}$. | ||
| کلیدواژهها | ||
| graph؛ Integral circulant graph؛ Eigenvalue؛ energy | ||
| مراجع | ||
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