Doob graph

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August undefined, 2024

WebRoads network built by expereinced engineers and modified by hundreds of contributors. Falavored with landmarks provided by users in addition to road events from doroob … 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.

Vertex-transitive graph - Wikipedia

Webconstructed 1-perfect codes in the Doob graphs of diameter 5. In the current paper, we show the existence of 1-perfect codes in D(m,n) in approxi-mately two-thirds (as µ→ ∞) … 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 pinja kunnossapito

Additive perfect codes in Doob graphs - Springer

Web1 mar 2024 · Doob graphs are an important family of distance-regular Cayley graphs. A necessary and sufficient condition for a Doob graph to admit perfect codes was recently … WebThe theory of graph spectra can, in a way, be considered as an attempt to utilize linear algebra including, in particular, the well-developed theory of matrices for the purposes of graph theory and its applications. to the theory of matrices; on the contrary, it has its own characteristic features and specific ways of reasoning fully justifying it to be treated as a … WebInteractive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more! pinja kukkakauppa

On Distance Laplacian Energy in Terms of Graph Invariants

Web1 dic 2024 · We display an action of the tetrahedron algebra on the standard module for any Hamming graph or Doob graph. To do this, we use some results of Brian Hartwig concerning tridiagonal pairs of ... Web3 apr 2024 · In the case of Doob graphs, the components of our quantum decompositions are the lowering, flat, and raising matrices. In this section, we describe the quantum … pinja konttinenWeb18 set 2024 · As an application of Theorem 2, we prove that the Doob graphs can be obtained from the Hamming graphs by switching many times. Not only so, compatibility suggests the possibility that some other pair of distance-regular graphs that have the same intersection array can be mapped to each other by switching. The Hamming Graphs and … haai essential mix

"Webcube, Doob graph, lollipop graph, barbell graph, distance spectrum, strongly regulargraph, optimistic graph, determinant, inertia, graph AMS subject classiﬁcations. 05C12, 05C31, 05C50, 15A15, 15A18, 15B48, 15B57 1 Introduction The distance matrix D(G) = [dij] of a graph G is the matrix indexed by the vertices of G where dij = d(vi,vj) " - Doob graph

Doob graph

Web1 nov 2024 · The direct product of the Hamming graph H (t, 4) with ℓ ≥ 1 copies of the Shrikande graph is called a Doob graph. One can check that Doob graphs are distance-regular and have the same intersection numbers as the Hamming graph H (t + 2 ℓ, 4). Yoshimi Egawa [16] proved that Doob graphs are the only graphs with this property. … Webgraphs H(N,q) from the point of view of algebraic combinatorics: H(N,4), N ≥ 2 are the only Hamming graphs that are not deﬁned as distance-regular graphs with given …

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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 … Web1 set 1995 · Egawa has shown that the Hamming graphs are determined by their parameters, unless λ equals 2. In that case the only possible graphs are the Doob …

Web26 mar 2015 · 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 (detailed definitions are … 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 …

Web13 giu 2024 · Abstract: 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, … Web1 ott 1979 · On Spectral Characterizations and Embeddings of Graphs Michael Doob* University of Manitoba Winnipeg, Manitoba, Canada and Dragog Cvetkovicf University of Belgrade Belgrade, Yugoslavia Submitted by Hans Schneider ABSTRACT The least eigenvalue of the 0-1 adjacency matrix of a graph is denoted A (G).

Web16 feb 2013 · The Doob graph is the graph given by the graph Cartesian product of copies of the Shrikhande graph with a Hamming graph . is cospectral with the Doob graph and …

Web13 lug 2024 · The Doob graph D(m, n), where m > 0, is a Cartesian product of m copies of the Shrikhande graph and n copies of the complete graph K 4 on four vertices. The … haaievinWebWe 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. haai essential mix tracklistWebDoob graphs are an important family of distance-regular Cayley graphs. A necessary and su cient condition for a Doob graph to admit perfect codes was recently given in [16], and all possible parameters of subgroup perfect codes in Doob graphs were described in [24]. haaihokduikWeb3 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 ). haaienvinnensoepWebIf 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}. … pinja koskinenWeb9 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. haaifiveWebGet full access to this article. View all available purchase options and get full access to this article. pinja koulutus