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Interval Colourings of Some Regular Graphs
Let G = (V,E) be an undirected graph without loops and multiple edges [1], V (G) and E(G) be the sets of vertices and edges of G, respectively. The degree of a vertex x ∈ V (G) is denoted by dG(x), the maximum degree of a vertex of G-by ∆(G), and the chromatic index [2] of G-by χ(G). A graph is regular, if all its vertices have the same degree. If α is a proper edge colouring of the graph G [3]...
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Let Γ be a regular graph with n vertices, diameter D, and d + 1 different eigenvalues λ > λ1 > · · · > λd. In a previous paper, the authors showed that if P (λ) > n − 1, then D ≤ d − 1, where P is the polynomial of degree d−1 which takes alternating values±1 atλ1, . . . , λd. The graphs satisfying P (λ) = n − 1, called boundary graphs, have shown to deserve some attention because of their rich ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1982
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90021-8