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In the mathematical field of graph theory, the Robertson graph or (4,5)-cage, is a 4-regular undirected graph with 19 vertices and 38 edges named after Neil Robertson.〔Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 237, 1976.〕 The Robertson graph is the unique (4,5)-cage graph and was discovered by Robertson in 1964.〔Robertson, N. "The Smallest Graph of Girth 5 and Valency 4." Bull. Amer. Math. Soc. 70, 824-825, 1964.〕 As a cage graph, it is the smallest 4-regular graph with girth 5. It has chromatic number 3, chromatic index 5, diameter 3, radius 3 and is both 4-vertex-connected and 4-edge-connected. The Robertson graph is also a Hamiltonian graph which possesses distinct directed Hamiltonian cycles. ==Algebraic properties== The Robertson graph is not a vertex-transitive graph and its full automorphism group is isomorphic to the dihedral group of order 24, the group of symmetries of a regular dodecagon, including both rotations and reflections.〔Geoffrey Exoo & Robert Jajcay, Dynamic cage survey, Electr. J. Combin. 15, 2008.〕 The characteristic polynomial of the Robertson graph is : : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Robertson graph」の詳細全文を読む スポンサード リンク
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