Results 21 to 30 of about 42,350 (268)
Characterizing Distance-Regularity of Graphs by the Spectrum [PDF]
Journal of Combinatorial Theory, Series A, 2005 We characterize the distance-regular Ivanov-Ivanov-Faradjev graph from the spectrum, and construct cospectral graphs of the Johnson graphs, Doubled Odd graphs, Grassmann graphs, Doubled Grassmann graphs, antipodal covers of complete bipartite graphs, and many of the Taylor graphs.We survey the known results on cospectral graphs of the Hamming graphs ...
Edwin R. van Dam +3 more
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A note on incomplete regular tournaments with handicap two of order n≡8(mod 16) [PDF]
Opuscula Mathematica, 2017 A \(d\)-handicap distance antimagic labeling of a graph \(G=(V,E)\) with \(n\) vertices is a bijection \(f:V\to \{1,2,\ldots ,n\}\) with the property that \(f(x_i)=i\) and the sequence of weights \(w(x_1),w(x_2),\ldots,w(x_n)\) (where \(w(x_i)=\sum_{x_i
Dalibor Froncek
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Electronic Journal of Graph Theory and Applications, 2015 We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones.
C. Dalfo, M. A. Fiol, M. Mitjana
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The matching polynomial of a distance-regular graph
International Journal of Mathematics and Mathematical Sciences, 2000 A distance-regular graph of diameter d has 2d intersection numbers that determine many properties of graph (e.g., its spectrum). We show that the first six coefficients of the matching polynomial of a distance-regular graph can also be determined from ...
Robert A. Beezer, E. J. Farrell
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The distance spectrum of corona and cluster of two graphs
AKCE International Journal of Graphs and Combinatorics, 2015 Let G be a connected graph with a distance matrix D. The D-eigenvalues {μ1,μ2,…,…,μp} of G are the eigenvalues of D and form the distance spectrum or D-spectrum of G.
G. Indulal, Dragan Stevanović
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D-magic strongly regular graphs
AKCE International Journal of Graphs and Combinatorics, 2020 For a set of distances D, a graph G on n vertices is said to be D-magic if there exists a bijection and a constant k such that for any vertex x, where is the D-neighbourhood set of x.
Rinovia Simanjuntak, Palton Anuwiksa
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On one infinite series of admissible intersection arrays of distance-regular graphs of diameter 5
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. One generalization of one known infinite series of admissible intersection arrays of a bipartite antipodal distance-regular graph is proposed for consideration.
I.T. Mukhamet'yanov
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Addressing graph products and distance-regular graphs
Discrete Applied Mathematics, 2017 Graham and Pollak showed that the vertices of any connected graph $G$ can be assigned $t$-tuples with entries in $\{0, a, b\}$, called addresses, such that the distance in $G$ between any two vertices equals the number of positions in their addresses where one of the addresses equals $a$ and the other equals $b$.
Sebastian M. Cioaba +4 more
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On Subgraphs in Distance-Regular Graphs [PDF]
Journal of Algebraic Combinatorics, 1992 A graph is distance-regular when it is simple and for any two vertices at distance \(j\), the numbers of vertices adjacent to one and at distance \(j- 1\) (resp. \(j\) and \(j+1)\) of the other are constant (depending on \(j\) only). First some necessary conditions are derived for distance- regularity of the subgraph of the geodesics joining two ...
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Distance-regularity and the spectrum of graphs [PDF]
Linear Algebra and its Applications, 1996 This paper considers the question whether a graph with the spectrum of a distance regular graph is distance regular. It has been known that the answer is affirmative if the distance regular graph has diameter not greater than 2, and that the answer is negative if the diameter is greater than 3.
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