The distance spectrum of two new operations of graphs
| Autor: | Zikai Tang, Renfang Wu, Hanlin Chen, Hanyuan Deng |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Transactions on Combinatorics, Vol 9, Iss 3, Pp 125-138 (2020) |
| Druh dokumentu: | article |
| ISSN: | 2251-8657 2251-8665 |
| DOI: | 10.22108/toc.2020.116372.1634 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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