Search Results for ""

A double-toroidal graph is a graph with graph genus 2 (West 2000, p. 266). Planar and toroidal graphs are therefore not double-toroidal. Some known double-toroidal graphs on ...

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 ...

The term "Euler graph" is sometimes used to denote a graph for which all vertices are of even degree (e.g., Seshu and Reed 1961). Note that this definition is different from ...

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 ...

The fractional edge chromatic number of a graph G is the fractional analog of the edge chromatic number, denoted chi_f^'(G) by Scheinerman and Ullman (2011). It can be ...

The Games graph is a strongly regular graph on 729 vertices with parameters (nu,k,lambda,mu)=(729,112,1,20). It is distance-regular but not distance-transitive with ...

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, ..., ...

For an undirected graph, an unordered pair of nodes that specify a line joining these two nodes are said to form an edge. For a directed graph, the edge is an ordered pair of ...

A connected graph is said to be highly irregular if the neighbors of each vertex have distinct vertex degrees. Highly irregular graphs exist on all orders except 3, 5 and 7, ...