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An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...

The all-pairs shortest path problem is the determination of the shortest graph distances between every pair of vertices in a given graph. The problem can be solved using n ...

Two nonisomorphic graphs are said to be chromatically equivalent (also termed "chromically equivalent by Bari 1974) if they have identical chromatic polynomials. A graph that ...

The inverse function of the logarithm, defined such that log_b(antilog_bz)=z=antilog_b(log_bz). The antilogarithm in base b of z is therefore b^z.

The binary logarithm log_2x is the logarithm to base 2. The notation lgx is sometimes used to denote this function in number theoretic literature. However, because Russian ...

There are several conflicting meanings associated with the notation lgx. In German and Russian literature, the notation lgx is used to mean the common logarithm log_(10)x. ...

lnx is the notation used in physics and engineering to denote the logarithm to base e, also called the natural logarithm, i.e., lnx=log_ex. The United States Department of ...

Given a distance-regular graph G with integers b_i,c_i,i=0,...,d such that for any two vertices x,y in G at distance i=d(x,y), there are exactly c_i neighbors of y in ...

Let c_k be the number of vertex covers of a graph G of size k. Then the vertex cover polynomial Psi_G(x) is defined by Psi_G(x)=sum_(k=0)^(|G|)c_kx^k, (1) where |G| is the ...

Cospectral graphs, also called isospectral graphs, are graphs that share the same graph spectrum. The smallest pair of isospectral graphs is the graph union C_4 union K_1 and ...