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The distance spectrum of two new operations of graphs | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 9، شماره 3، آذر 2020، صفحه 125-138 اصل مقاله (399.5 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.116372.1634 | ||
| نویسندگان | ||
| Zikai Tang؛ Renfang Wu* ؛ Hanlin Chen؛ Hanyuan Deng* | ||
| Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China | ||
| چکیده | ||
| Let $G$ be a connected graph with vertex set $V(G)=\{v_1, v_2,\ldots,v_n\}$. The distance matrix $D=D(G)$ of $G$ is defined so that its $(i,j)$-entry is equal to the distance $d_G(v_i,v_j)$ between the vertices $v_i$ and $v_j$ of $G$. The eigenvalues ${\mu_1, \mu_2,\ldots,\mu_n}$ of $D(G)$ are the $D$-eigenvalues of $G$ and form the distance spectrum or the $D$-spectrum of $G$, denoted by $Spec_D(G)$. In this paper, we introduce two new operations $G_1\blacksquare_k G_2$ and $G_1\blacklozenge_k G_2$ on graphs $G_1$ and $G_2$, and describe the distance spectra of $G_1\blacksquare_k G_2$ and $G_1\blacklozenge_k G_2$ of regular graphs $G_1$ and $G_2 $ in terms of their adjacency spectra. By using these results, we obtain some new integral adjacency spectrum graphs, integral distance spectrum graphs and a number of families of sets of noncospectral graphs with equal distance energy. | ||
| کلیدواژه‌ها | ||
| Adjacency spectrum؛ Distance spectrum؛ Distance energy | ||
| مراجع | ||
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