A geometrical characterization of strongly regular graphs
نویسندگان
چکیده
منابع مشابه
Strongly regular graphs
Strongly regular graphs form an important class of graphs which lie somewhere between the highly structured and the apparently random. This chapter gives an introduction to these graphs with pointers to more detailed surveys of particular topics.
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We give a sufficient condition for a distance-regular graph to be Hamiltonian. In particular, the Petersen graph is the only connected nonHamiltonian strongly regular graph on fewer than 99 vertices.
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Strongly regular graphs lie on the cusp between highly structured and unstructured. For example, there is a unique strongly regular graph with parameters (36,10,4,2), but there are 32548 non-isomorphic graphs with parameters (36,15,6,6). (The first assertion is a special case of a theorem of Shrikhande, while the second is the result of a computer search by McKay and Spence.) In the light of th...
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A graph Γ with diameter d is strongly distance-regular if Γ is distanceregular and its distance-d graph Γd is strongly regular. The known examples are all the connected strongly regular graphs (i.e. d = 2), all the antipodal distanceregular graphs, and some distance-regular graphs with diameter d = 3. The main result in this paper is a characterization of these graphs (among regular graphs with...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2012.05.040