Search Results for ""

Let c_k be the number of edge covers of a graph G of size k. Then the edge cover polynomial E_G(x) is defined by E_G(x)=sum_(k=0)^mc_kx^k, (1) where m is the edge count of G ...

Euler (1772ab) conjectured that there are no positive integer solutions to the quartic Diophantine equation A^4=B^4+C^4+D^4. This conjecture was disproved by Elkies (1988), ...

An Eulerian cycle, also called an Eulerian circuit, Euler circuit, Eulerian tour, or Euler tour, is a trail which starts and ends at the same graph vertex. In other words, it ...

A factor is a portion of a quantity, usually an integer or polynomial that, when multiplied by other factors, gives the entire quantity. The determination of factors is ...

A fiveleaper graph is a graph formed by all possible moves of a hypothetical chess piece called a "fiveleaper" which moves analogously to a knight except that it is ...

Let C^*(u) denote the number of nowhere-zero u-flows on a connected graph G with vertex count n, edge count m, and connected component count c. This quantity is called the ...

Flower graphs are a name given in this work to the generalization of the flower snarks J_n for positive n=5, 7, 9, ... to all integer n>=5. They are illustrated above for n=5 ...

The Floyd-Warshall algorithm, also variously known as Floyd's algorithm, the Roy-Floyd algorithm, the Roy-Warshall algorithm, or the WFI algorithm, is an algorithm for ...

A generalized Moore graph is a regular graph of degree r where the counts of vertices at each distance d=0, 1, ... from any vertex are 1, r, r(r-1), r(r-1)^2, r(r-1)^3, ..., ...

Ore (1962) noted that not only does a tree possesses a unique shortest path between any two vertices, but that there also exist also other connected graphs having the same ...