منابع مشابه
The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters
We prove a conjecture by Van Dam & Sotirov on the smallest eigenvalue of (distance-j) Hamming graphs and a conjecture by Karloff on the smallest eigenvalue of (distance-j) Johnson graphs. More generally, we study the smallest eigenvalue and the second largest eigenvalue in absolute value of the graphs of the relations of classical P and Q-polynomial association schemes.
متن کاملClassical Distance-Regular Graphs of Negative Type
Brouwer, Cohen, and Neumaier found that the intersection numbers of most known families of distance-regular graphs could be described in terms of four parameters (d, b, :, ;) [2, pp. ix, 193]. They invented the term classical to describe those graphs for which this could be done. All classical distance-regular graphs with b=1 are classified by Y. Egawa, A. Neumaier, and P. Terwilliger in a sequ...
متن کاملEdge-distance-regular graphs are distance-regular
A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph Γ is distance-regular and homogeneous. More precisely, Γ is edge-distance-regular if and only if it is bipartite distance-reg...
متن کاملDistance-two labellings of Hamming graphs
Let j ≥ k ≥ 0 be integers. An `-L(j, k)-labelling of a graph G = (V , E) is a mapping φ : V → {0, 1, 2, . . . , `} such that |φ(u)−φ(v)| ≥ j if u, v are adjacent and |φ(u)−φ(v)| ≥ k if they are distance two apart. Let λj,k(G) be the smallest integer ` such that G admits an `-L(j, k)-labelling. Define λj,k(G) to be the smallest ` if G admits an `-L(j, k)-labelling with φ(V ) = {0, 1, 2, . . . , ...
متن کاملOn Robust Colorings of Hamming-Distance Graphs
Hq(n, d) is defined as the graph with vertex set Zq and where two vertices are adjacent if their Hamming distance is at least d. The chromatic number of these graphs is presented for various sets of parameters (q, n, d). For the 4-colorings of the graphs H2(n, n − 1) a notion of robustness is introduced. It is based on the tolerance of swapping colors along an edge without destroying properness...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1990
ISSN: 0095-8956
DOI: 10.1016/0095-8956(90)90071-7