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The study of how the intrinsic structure of graphs ensures certain types of properties (e.g., clique-formation and graph colorings) under appropriate conditions.

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

Let sumu_k be a series with positive terms and let f(x) be the function that results when k is replaced by x in the formula for u_k. If f is decreasing and continuous for ...

Vardi's integral is the beautiful definite integral int_(pi/4)^(pi/2)lnlntanxdx = pi/2ln[sqrt(2pi)(Gamma(3/4))/(Gamma(1/4))] (1) = pi/4ln[(4pi^3)/(Gamma^4(1/4))] (2) = ...

The q-analog of integration is given by int_0^1f(x)d(q,x)=(1-q)sum_(i=0)^inftyf(q^i)q^i, (1) which reduces to int_0^1f(x)dx (2) in the case q->1^- (Andrews 1986 p. 10). ...

A quasi-cubic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

Clausen's integral, sometimes called the log sine integral (Borwein and Bailey 2003, p. 88) is the n=2 case of the S_2 Clausen function Cl_2(theta) = ...

A graph G with m edges is said to be elegant if the vertices of G can be labeled with distinct integers (0,1,2,...,m) in such a way that the set of values on the edges ...

Cubic graphs, also called trivalent graphs, are graphs all of whose nodes have degree 3 (i.e., 3-regular graphs). Cubic graphs on n nodes exists only for even n (Harary 1994, ...

A spider graph, spider tree, or simply "spider," is a tree with one vertex of degree at least 3 and all others with degree at most 2. The numbers of spiders on n=1, 2, ... ...