The distance spectrum of two new operations of graphs
عنوان مقاله: The distance spectrum of two new operations of graphs
شناسه ملی مقاله: JR_COMB-9-3_001
منتشر شده در در سال 1399
شناسه ملی مقاله: JR_COMB-9-3_001
منتشر شده در در سال 1399
مشخصات نویسندگان مقاله:
Zikai Tang - Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, Hunan ۴۱۰۰۸۱, P. R. China
Renfang Wu - Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, Hunan ۴۱۰۰۸۱, P. R. China
Hanlin Chen - Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, Hunan ۴۱۰۰۸۱, P. R. China
Hanyuan Deng - Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, Hunan ۴۱۰۰۸۱, P. R. China
خلاصه مقاله:
Zikai Tang - Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, Hunan ۴۱۰۰۸۱, P. R. China
Renfang Wu - Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, Hunan ۴۱۰۰۸۱, P. R. China
Hanlin Chen - Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, Hunan ۴۱۰۰۸۱, P. R. China
Hanyuan Deng - Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Sta- tistics, Hunan Normal University, Changsha, Hunan ۴۱۰۰۸۱, P. R. China
Let $G$ be a connected graph with vertex set $V(G)=\{v_۱, v_۲,\ldots,v_n\}$. 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 ${\mu_۱, \mu_۲,\ldots,\mu_n}$ 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 $G_۱\blacksquare_k G_۲$ and $G_۱\blacklozenge_k G_۲$ on graphs $G_۱$ and $G_۲$, and describe the distance spectra of $G_۱\blacksquare_k G_۲$ and $G_۱\blacklozenge_k G_۲$ of regular graphs $G_۱$ and $G_۲ $ 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.
کلمات کلیدی: Adjacency spectrum, Distance spectrum, Distance energy
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1194846/