The identification of clusters, well-connected components in a graph, is useful in many applications from biological function prediction to social community detection. However, ...
In 1988, Seiya Negami published a conjecture stating that a graph G has a finite planar cover (i.e. a homomorphism from some planar graph onto G which maps the vertex neighbourhoo...
For a directed graph G without loops or parallel edges, let (G) denote the size of the smallest feedback arc set, i.e., the smallest subset X E(G) such that G \ X has no directed...
We prove that for graphs of order n, minimum degree 2 and girth g 5 the domination number satisfies 1 3 + 2 3g n. As a corollary this implies that for cubic graphs of order n ...
For graphs G and H, let G H denote their Cartesian sum. This paper investigates the chromatic number and the circular chromatic number for GH. It is proved that (G H) max{ c(G)...