جستجوی مقالات مرتبط با کلیدواژه « bipartite kneser graph » در نشریات گروه « ریاضی »
تکرار جستجوی کلیدواژه «bipartite kneser graph» در نشریات گروه «علوم پایه»-
For any given $n,k \in \mathbb{N}$ with $ 2k < n, $ the $bipartite\ Kneser \ graph$ $H(n, k)$ is defined as the graph whose vertex set is the family of $k$-subsets and ($n-k$)-subsets of $[n] = \{1, 2,\dots, n\}, $ in whichany two vertices are adjacent if and only if one of them is a subset of the other.In this paper, we study some algebraic properties of the bipartite Kneser graph $H(n, k)$. In particular, we determine the values of $n,k$, for which the bipartite Knesergraph $H(n,k)$ is a Cayley graph.Keywords: Bipartite Kneser Graph, Vertex-Transitive Graph, Automorphism}
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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 its distance eigenvalues are integers. In this paper, we introduce some new classes of distance integral graphs. In particular, we show that if $n,k$ are integers such that $n \geq 3k >0$, then the bipartite Kneser graph $H(n,k)$ is distance integral. Moreover, we determine the distance spectrum of $H(n,k)$. Also, we show that every distance regular integral graph is distance integral.Keywords: Distance integral, vertex-transitive, distance regular, bipartite Kneser graph}
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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}
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