جستجوی مقالات مرتبط با کلیدواژه « Distance spectrum » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه «Distance spectrum» در نشریات گروه «علوم پایه»-
The distance eigenvalues of a connected graph $G$ are the eigenvalues of its distance matrix$D(G)$. A graph is called distance integral if all of itsdistance eigenvalues are integers.Let $n$ and $k$ be integers with $n>2k, kgeq1$. The bipartite Kneser graph $H(n,k)$ is the graph with the set of all $k$ and $n-k$ subsets of the set $[n]={1,2,...,n}$ as vertices, in which two vertices are adjacent if and only if one of them is a subset of the other. In this paper, we determine the distance spectrum of $H(n,1)$. Although the obtained result is not new cite{12}, but our proof is new. The main tool that we use in our work is the orbit partition method in algebraic graph theory for finding the eigenvalues of graphs. We introduce a new method fordetermining the distance spectrum of $H(n,1)$ and show howa quotient matrix can contain all distance eigenvalues ofa graph.
Keywords: Distance matrix, distance spectrum, orbit partition, bipartite Kneser graph} -
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 $G_1blacksquare_k G_2$ and $G_1blacklozenge_k G_2$ on graphs $G_1$ and $G_2$, and describe the distance spectra of $G_1blacksquare_k G_2$ and $G_1blacklozenge_k G_2$ 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.Keywords: Adjacency spectrum, Distance spectrum, Distance energy}
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Journal of Algebraic Structures and Their Applications, Volume:4 Issue: 1, Winter - Spring 2017, PP 51 -56The D-eigenvalues {µ1, ,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated line graphs of G are of diameter 2 and that ED(\overline{Lk(G)}), k≥2 depends only on p and r. This result leads to the construction of regular D-equi energetic pair of graphs.Keywords: Distance spectrum, Distance energy, Line graphs}
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