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A fraction containing each of the digits 1 through 9 is called a pandigital fraction. The following table gives the number of pandigital fractions which represent simple unit ...

There are several different definitions of the barbell graph. Most commonly and in this work, the n-barbell graph is the simple graph obtained by connecting two copies of a ...

The m-book graph is defined as the graph Cartesian product B_m=S_(m+1) square P_2, where S_m is a star graph and P_2 is the path graph on two nodes. The generalization of the ...

The bull graph is a simple graph on 5 nodes and 5 edges whose name derives from its resemblance to a schematic illustration of a bull or ram (whose face is the triangle and ...

The gear graph, also sometimes known as a bipartite wheel graph (Brandstädt et al. 1987), is a wheel graph with a graph vertex added between each pair of adjacent graph ...

Ball and Coxeter (1987, pp. 277-278) define the ladder graph nP_2, here called the ladder rung graph, of order n as the graph union of n copies of the path graph P_2. The ...

The n-pan graph is the graph obtained by joining a cycle graph C_n to a singleton graph K_1 with a bridge. The n-pan graph is therefore isomorphic with the (n,1)-tadpole ...

The nth cubic number n^3 is a sum of n consecutive odd numbers, for example 1^3 = 1 (1) 2^3 = 3+5 (2) 3^3 = 7+9+11 (3) 4^3 = 13+15+17+19, (4) etc. This identity follows from ...

A triangle with rows containing the numbers {1,2,...,n} that begins with 1, ends with n, and such that the sum of each two consecutive entries being a prime. Rows 2 to 6 are ...

A prime p is called a Wolstenholme prime if the central binomial coefficient (2p; p)=2 (mod p^4), (1) or equivalently if B_(p-3)=0 (mod p), (2) where B_n is the nth Bernoulli ...