1 citations · 3 across the 10 of their papers we have counts for
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Size of bipartite graphs with given diameter and connectivity constraints
Sonwabile Mafunda
In the first part of this paper we determine the maximum size of a (finite, simple, connected) bipartite graph of given order, diameter , and connectivity . It was shown by A…
A Note on Distance-Fall Colorings
Wayne Goddard, Sonwabile Mafunda
We say a proper coloring of a graph is distance- fall if every vertex is within distance of at least one vertex of every color. We show that if is a connected graph of o…
On Proximity and other Distance Parameters in Planar Graphs
Peter Dankelmann, Sonwabile Mafunda, Sufiyan Mallu
Let be a connected graph. The average distance of a vertex of is the arithmetic mean of the distances from to all other vertices of . The proximity and remotenes…
Proximity and Radius in Outerplanar Graphs with Bounded Faces
Peter Dankelmann, Sonwabile Mafunda, Sufiyan Mallu
Let be a finite, connected graph and a vertex of . The average distance and the eccentricity of in are defined as the arithmetic mean and the maximum, respective…
Remoteness of graphs with given size and connectivity constraints
Peter Dankelmann, Sonwabile Mafunda, Sufiyan Mallu
Let be a finite, simple connected graph. The average distance of a vertex of is the arithmetic mean of the distances from to all other vertices of . The remotene…
Paint cost spectrum of perfect -ary trees
Sonwabile Mafunda, Jonathan L. Merzel, K. E. Perry +1
We determine the paint cost spectrum for perfect -ary trees. A coloring of the vertices of a graph with colors is said to be \emph{-distinguishing} if only the trivia…