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On the skew spectral moments of graphs | ||
| Transactions on Combinatorics | ||
| مقاله 4، دوره 6، شماره 1، خرداد 2017، صفحه 47-54 اصل مقاله (238.13 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2017.20737 | ||
| نویسندگان | ||
| Fatemeh Taghvaee؛ Gholam Hossein Fath-Tabar* | ||
| University of Kashan | ||
| چکیده | ||
| Let $G$ be a simple graph, and $G^{\sigma}$ be an oriented graph of $G$ with the orientation $\sigma$ and skew-adjacency matrix $S(G^{\sigma})$. The $k-$th skew spectral moment of $G^{\sigma}$, denoted by $T_k(G^{\sigma})$, is defined as $\sum_{i=1}^{n}( \lambda_{i})^{k}$, where $\lambda_{1}, \lambda_{2},\cdots, \lambda_{n}$ are the eigenvalues of $G^{\sigma}$. Suppose $G^{\sigma_1}_{1}$ and $G^{\sigma_2}_{2}$ are two digraphs. If there exists an integer $k$, $1 \leq k \leq n-1$, such that for each $i$, $0 \leq i \leq k-1$, $T_i(G^{\sigma_1}_{1}) = T_i(G^{\sigma_2}_{2})$ and $T_k(G^{\sigma_1}_{1}) <T_k(G^{\sigma_ 2}_{2})$ then we write $G^{\sigma_1}_{1} \prec_{T} G^{\sigma_2}_{2}$. In this paper, we determine some of the skew spectral moments of oriented graphs. Also we order some oriented unicyclic graphs with respect to skew spectral moment. | ||
| کلیدواژهها | ||
| Oriented graph؛ skew spectral moment؛ skew eigenvalue؛ $T$-order؛ skew characteristic polynomial | ||
| مراجع | ||
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[7] G. H. Fath-Tabar, A. R. Ashra and D. Stevanovic, Sp ectral Prop erties of Fullerenes, J. Comput. Theor. Nanosci., 9 (2012) 327-329.
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[11] F. Taghvaee and A. R. Ashra , Comparing fullerenes by sp ectral moments, J. Nanosci. Nanotechnol., 16 (2016) 1-4.
[12] F. Taghvaee and G. H. Fath-Tabar, Signless Laplacian sp ectral moments of graphs and ordering some graphs with resp ect to them, Alg. Struc. Appl., 1 (2014) 133-141.
[13] F. Taghvaee and G. H. Fath-Tabar, Relationship b etween co efficients of characteristic p olynomial and matching p olynomial of regular graphs and its applications, Iranian J. Math. Chem., 8 (2017) 7-24.
[14] Y. P. Wu and H. Q. Liu, Lexicographical ordering by sp ectral moments of trees with a prescrib ed diameter, Linear Algebra Appl., 433 (2010) 1707-1713. | ||
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