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The edge chromatic number, sometimes also called the chromatic index, of a graph G is fewest number of colors necessary to color each edge of G such that no two edges ...

A number which is simultaneously pentagonal and hexagonal. Let P_n denote the nth pentagonal number and H_m the mth hexagonal number, then a number which is both pentagonal ...

A number which is simultaneously octagonal and heptagonal. Let O_m denote the mth octagonal number and H_n the nth heptagonal number, then a number which is both octagonal ...

A number which is simultaneously octagonal and pentagonal. Let O_n denote the nth octagonal number and P_m the mth pentagonal number, then a number which is both octagonal ...

A number which is simultaneously octagonal and square. Let O_n denote the nth octagonal number and S_m the mth square number, then a number which is both octagonal and square ...

A figurate number which is constructed as a centered cube with a square pyramid appended to each face, RhoDod_n = CCub_n+6P_(n-1)^((4)) (1) = (2n-1)(2n^2-2n+1), (2) where ...

A figurate number which is constructed as an octahedral number with a square pyramid removed from each of the six graph vertices, TO_n = O_(3n-2)-6P_(n-1)^((4)) (1) = ...

A Sierpiński number of the first kind is a number of the form S_n=n^n+1. The first few are 2, 5, 28, 257, 3126, 46657, 823544, 16777217, ... (OEIS A014566). Sierpiński proved ...

The lower independence number i(G) of a graph G is the minimum size of a maximal independent vertex set in G. The lower indepedence number is equiavlent to the "independent ...

The path covering number (or path-covering number; Slater 1972) of a graph G, variously denoted as summarized below, is the minimum number of vertex-disjoint paths that cover ...