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- W1973994998 abstract "A tetrahedral graph may be defined as a graph G , whose vertices may be identified with the n(n −1)( n −2)/6 unordered triplets on n symbols, such that two vertices are adjacent if and only if the corresponding triplets have two symbols in common. If d(x,y) denotes the distance between two vertices x and y Δ(x, y) denotes the number of vertices adjacent to both x and y , then a tetrahedral graph G has the following properties: (b 1 ) The number of vertices is n(n −1)( n −2)/6. (b 2 ) G is connected and regular of valence 3( n −3). (b 3 ) For any two adjacent vertices x and y, Δ(x, y)=n −2. (b 4 ) Δ(x,y) =4 if d(x, y) =2. We show that, if n >16, then any graph G (without loops and with utmost one edge connecting two vertices) having the properties (b 1 )−(b 4 ) must be a tetrahedral graph." @default.
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- W1973994998 date "1967-12-01" @default.
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- W1973994998 title "A characterization of tetrahedral graphs" @default.
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- W1973994998 doi "https://doi.org/10.1016/s0021-9800(67)80104-2" @default.
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