Hoffman-singleton graph
NettetThe Hoffman-Singleton graph is the graph on 50 nodes and 175 edges that is the only regular graph of vertex degree 7, diameter 2, and girth 5. It is the unique -cage graph … Nettet14. okt. 2024 · I have a python code need to draw a networkx graph, it can output normally. However, I got some problems in the following code. import networkx as nx import matplotlib.pyplot as plt import matplotl...
Hoffman-singleton graph
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Nettetgraph_atlas# graph_atlas (i) [source] # Returns graph number i from the Graph Atlas. For more information, see graph_atlas_g(). Parameters: i int. The index of the graph from the atlas to get. The graph at index 0 is assumed to be the null graph. Returns: list. A list of Graph objects, the one at index i corresponding to the graph i in the ... NettetThe Higman-Sims graph can be constructed from the Hoffman-Singleton graph by treating the latter's 100 independent vertex sets of size 15 as vertices and connecting by edges those pairs of independent sets which share ... Hafner, P. R. "On the Graphs of Hoffman-Singleton and Higman-Sims." Elec. J. Combin. 11, R77, 1-32, 2004.Higman, …
NettetHere is a good reference from 2010: Search for properties of the missing Moore graph which shows among other things that if such a graph exists then it has automorphism group of order at most 375. later Since we have new interest I'll … NettetHoffman AJ, Singleton RR (1960) On moore graphs with diameters 2 and 3. IBM J Res Dev 4(5):497---504 Google Scholar Digital Library; Dally WJ, Towles BP (2004) Principles and practices of interconnection networks. Morgan Kaufmann, Massachusetts Google Scholar Digital Library; Jantsch A, Tenhunen H et al (2003) Networks on chip, vol 396.
NettetIn addition to being a Moore graph, the Hoffman-Singleton graph is part of a family of non-Cayley transitive graphs with order 2q2, where q ≡ 1 (mod 4) is a prime power, … NettetThere is a beautiful way to construct the Hoffman–Singleton graph by connecting 5 pentagons to 5 pentagrams. 1 February, 2016 in Graphs, Groups, Images Library. Balaban 11-Cage. This picture shows part of a graph called the Balaban 11-cage. A (3,11)-graph is a simple graph where every vertex has 3 neighbors and the shortest …
NettetConstruction From M22 graph. Take the M22 graph, a strongly regular graph srg(77,16,0,4) and augment it with 22 new vertices corresponding to the points of …
NettetDownload scientific diagram (a) A construction of the Petersen graph by lifting with the group C5. (b) By lifting the described graph with the group C 2 5 , we get the Hoffman-Singleton graph. eft crickent lighterNettetThe Hoffman-Singleton graph HS may be described as the unique MOORE graph of degree 7 and diameter 2 [2], or as the unique 7-regular graph of order 50 with girth 5 [1, p. 189]. It may be constructed as follows, where a hep-tad is a set of seven triples which may be taken as the lines of a Fano plane whose eft credit canada gainstps meaningNettet18. mai 2013 · Hoffman-Singleton graph. We’ve shown that there exist graphs of degree 2 and 3 with these properties. The next graph has degree 7, and is known as the … foia und wasserNettet15. jun. 2024 · Construction From M22 graph. Take the M22 graph, a strongly regular graph srg(77,16,0,4) and augment it with 22 new vertices corresponding to the points … eft crashing 2023Nettetlollipop_graph. #. lollipop_graph(m, n, create_using=None) [source] #. Returns the Lollipop Graph; K_m connected to P_n. This is the Barbell Graph without the right barbell. Parameters: m, nint or iterable container of nodes (default = 0) If an integer, nodes are from range (m) and range (m,m+n) . If a container of nodes, those nodes appear in ... foia virginia department of healthNettetb) A split into two Hoffman-Singleton graphs. There are 352 of these, forming a single orbit. The stabilizer is U 3 (5).2 with vertex orbit size 100. (That such splits exist is … foia verification of identityNettetIn our work, we give a straightforward counting argument showing that the Hoffman-Singleton graph answers this question in the affirmative for the case of girth 5. It is then shown that certain generalized polygons, constructed of sufficiently large order, are also PRCF-bad, thus proving the existence of PRCF-bad graphs of girth 6, 8, 12, and 16. foia vs section 83