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Consider a broadcast scheme on a connected graph from an originator vertex v in a graph G consisting of a sequence of parallel calls starting from v. In each time step, every ...

The voter model is a simple mathematical model of opinion formation in which voters are located at the nodes of a network, each voter has an opinion (in the simplest case, 0 ...

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

The Krackhardt kite is the simple graph on 10 nodes and 18 edges illustrated above. It arises in social network theory. It is implemented in the Wolfram Language as ...

Algorithmic graph theory is the study of graph traversal and generation and the complexity of these operations. Topics in algorithmic graph theory include Eulerian and ...

Consider a network of n resistors R_i so that R_2 may be connected in series or parallel with R_1, R_3 may be connected in series or parallel with the network consisting of ...

If k|n, then the complete k-uniform hypergraph on n vertices decomposes into 1-factors, where a 1-factor is a set of n/k pairwise disjoint k-sets. Brouwer and Schrijver ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

A branch of mathematics which encompasses many diverse areas of minimization and optimization. Optimization theory is the more modern term for operations research. ...

In combinatorial mathematics, the series-parallel networks problem asks for the number of networks that can be formed using a given number of edges. The edges can be ...