More on Moore graphs
نویسندگان
چکیده
منابع مشابه
More Equienergetic Signed Graphs
The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy. In the literature the construction of equienergetic signed graphs are reported. In this paper we obtain the characteristic polynomial and energy of the join of two signed graphs and thereby we give another construction ...
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We prove here a well known result in graph theory, originally proved by Hoffman and Singleton, that any non-trivial Moore graph of diameter 2 is regular of degree k = 2, 3, 7 or 57. The existence (and uniqueness) of these graphs is known for k = 2, 3, 7 while it is still an open problem if there is a moore graph of degree 57 or not.
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Let C2k denote the cycle of length 2k and Cg = {C3, C4, . . . , Cg}. The girth of a graph G containing a cycle is the length of a shortest cycle in G, so a graph has girth at least g + 1 if it is Cg-free. The distance between vertices u and v in a graph G, denoted dG(u, v) is the minimum length of a uv-path in G. Then dG(·, ·) is a metric on V (G). The diameter of a connected graph G is max{dG(...
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Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge set E(G). The (first) edge-hyper Wiener index of the graph G is defined as: $$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=frac{1}{2}sum_{fin E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$ where de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(f,g|G). In thi...
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In any spatially discrete model of pedestrian motion which uses a regular lattice as basis, there is the question of how the symmetry between the different directions of motion can be restored as far as possible but with limited computational effort. This question is equivalent to the question " How important is the orientation of the axis of discretization for the result of the sim-ulation? " ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2013
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2012.10.003