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A planted tree is a rooted tree whose root vertex has vertex degree 1. The number of planted trees of n nodes is T_(n-1), where T_(n-1) is the number of rooted trees of n-1 ...

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

The Q-chromatic polynomial, introduced by Birkhoff and Lewis (1946) and termed the "Q-chromial" by Bari (1974), is an alternate form of the chromatic polynomial pi(x) defined ...

The Latin prefix quadri- is used to indicate the number 4, for example, quadrilateral, quadrant, etc. However, it also very commonly used to denote objects involving the ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution ...

A partition whose conjugate partition is equivalent to itself. The Ferrers diagrams corresponding to the self-conjugate partitions for 3<=n<=10 are illustrated above. The ...

Let a simple graph G have n vertices, chromatic polynomial P(x), and chromatic number chi. Then P(G) can be written as P(G)=sum_(i=0)^ha_i·(x)_(p-i), where h=n-chi and (x)_k ...

A stack polyomino is a self-avoiding convex polyomino containing two adjacent corners of its minimal bounding rectangle. The number of stack polyominoes with perimeter 2n+4 ...

Triskaidekaphobia is the fear of 13, a number commonly associated with bad luck in Western culture. While fear of the number 13 can be traced back to medieval times, the word ...