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The mean distance of a (connected) graph is the mean of the elements of its graph distance matrix. Closed forms for some classes of named graphs are given in the following ...

If f(z) is continuous in a region D and satisfies ∮_gammafdz=0 for all closed contours gamma in D, then f(z) is analytic in D. Morera's theorem does not require simple ...

The rhombic triacontahedral graph is Archimedean dual graph which is the skeleton of the rhombic triacontahedron, great rhombic triacontahedron, and small triambic ...

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 ...

For a scalar function f over a surface parameterized by u and v, the surface integral is given by Phi = int_Sfda (1) = int_Sf(u,v)|T_uxT_v|dudv, (2) where T_u and T_v are ...

A transposition graph G_n is a graph whose nodes correspond to permutations and edges to permutations that differ by exactly one transposition (Skiena 1990, p. 9, Clark ...

Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

Let [arg(f(z))] denote the change in the complex argument of a function f(z) around a contour gamma. Also let N denote the number of roots of f(z) in gamma and P denote the ...

The n-wheel complement graph W^__n is the graph complement of the n-wheel graph. For n>4, W^__n is isomorphic to the graph disjoint union of a circulant graph ...

A white bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board), when ...