Consider an n-vertex graph G = (V, E) of maximum degree ∆, and suppose that each vertex v ∈ V hosts a processor. The processors are allowed to communicate only with their neig...
Abstract. We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according ...
This paper proposes a method for reducing the maximum degree of vertices in graphs that maintain optimal broadcast time when a vertex can call a vertex at distance at most k durin...
In edge colouring it is often useful to have information about the degree distribution of the neighbours of a given vertex. For example, the well known Vizing's Adjacency Lem...
The communities of a social network are sets of vertices with more connections inside the set than outside. We theoretically demonstrate that two commonly observed properties of s...