Doob graph
WebGet full access to this article. View all available purchase options and get full access to this article. Web1 ott 2009 · In this paper, we first prove that the graph K n m and its complement are determined by their adjacency spectra, and by their Laplacian spectra. Then we prove that U n, p is determined by its Laplacian spectrum, as well as its adjacency spectrum if p is odd, and find all its cospectral graphs for U n, 4.
Doob graph
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Web23 lug 2014 · The Doo b graph D (m, n) is a distance regular graph of diameter 2 m + n with the same parameters as the Hamming graph H (2 m + n, 4). As noted in [9], nontrivial e … WebThis graph is called a Doob graph if m > 0, while D(0,n) is a 4-ary Hamming graph. Note that D(m,n) is a Cayley graph of (Z2 4) m ×(Z2 2) n, with the corresponding connecting set. Given a graph G, by VG we denote its set of vertices. Two subsets of VG are said to be equivalent if there is a graph automorphism that maps one subset to the other.
Web29 nov 2024 · The Doob graph D(m, n) is the Cartesian product of m copies of the Shrikhande graph and n copies of the complete graph of order 4, where the Shrikhande … Web9 ott 2024 · We solve the problem of existence of perfect codes in the Doob graph. It is shown that 1-perfect codes in the Doob graph D(m,n) exist if and only if 6m+3n+1 is a power of 2; that is, if the size of a 1-ball divides the number of vertices. READ FULL TEXT
WebIn the mathematical field of graph theory, a vertex-transitive graph is a graph G in which, given any two vertices v 1 and v 2 of G, there is some automorphism: such that =. In … WebThe Doob graph D(m,n) is the Cartesian product of m copies of the Shrikhande graph and n copies of the complete graph of order 4, where the Shrikhande graph is a strongly …
WebIf m > 0, then D(m,n) is called a Doob graph. The Shrikhande graph Sh is the Cayley graph of the additive group Z2+ 4of Z 2with the generating set S = {01,30,33,03,10,11}. That is, the vertex set is the set of elements of Z2 4, two elements being adjacent if and only if their difference is in S.
WebGeneralizations of Magic Graphs MICHAEL DOOB Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada Communicated by W. T. Tutte Received February 14, 1974 A graph is magic if the edges are lab&d with distinct nomregative real numbers such that the sum of the labels incident to each vertex is the same. p5r life draining spiritWeb13 giu 2024 · The Doob graph D (m,n) is the Cartesian product of m>0 copies of the Shrikhande graph and n copies of the complete graph of order 4. Naturally, D (m,n) can be represented as a Cayley graph on the additive group (Z_4^2)^m × … p5r jose fight rewardhttp://www.doroob.net/ p5r key itemsWeb9 ott 2024 · We solve the problem of existence of perfect codes in the Doob graph. It is shown that 1-perfect codes in the Doob graph D(m,n) exist if and only if 6m+3n+1 is a power of 2; that is, if the size of a 1-ball divides the number of vertices. Keywords: perfect codes, distance-regular graphs, Doob graphs, Eisenstein-Jacobi integers. jenks southeast elementary calendarWeb1 mag 2000 · Doob graphs are distance-regular graphs having the same parameters as the quaternary Hamming graphs. Delsarte's generalization of Lloyd's theorem implies … jenks staff directoryWeb3 apr 2024 · This graph was first introduced by Doob in 1972 (see [ 4 ]). The graph D ( n , m) is distance-regular and has the same intersection numbers as H (2n+m,4) (see [ 5 ]). We note that H ( n , q) and D ( n , m) have integral eigenvalues. In this section, objects in reference to the Doob graph D ( n , m) are labeled with ( n , m ). p5r madarame fightWeb13 giu 2024 · The Doob graph D(m,n) is the Cartesian product of m>0 copies of the Shrikhande graph and n copies of the complete graph of order 4. Naturally, D(m,n) can … jenks southeast school calendar