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- Peter Dankelmann, David P. Day, David Erwin, Simon Mukwembi, Henda C. Swart
- Discrete Mathematics
- 2009

Let G be a graph and S âŠ† V (G). For each vertex u âˆˆ S and for each v âˆˆ V (G) âˆ’ S, we define d(u, v) = d(v, u) to be the length of a shortest path in ã€ˆV (G)âˆ’(Sâˆ’{u})ã€‰ if such a path exists, andâˆžâ€¦ (More)

- Simon Mukwembi
- Discrete Mathematics
- 2010

The inverse degree r(G) of a finite graph G = (V, E) is defined as r(G) = vâˆˆV 1 deg v , where deg v is the degree of vertex v. We establish inequalities concerning the sum of the diameter and theâ€¦ (More)

- Peter Dankelmann, Ivan Gutman, Simon Mukwembi, Henda C. Swart
- Discrete Mathematics
- 2009

If G is a connected graph, then the distance between two edges is, by definition, the distance between the corresponding vertices of the line graph of G. The edge-Wiener index We of G is then equalâ€¦ (More)

- M. J. Morgan, Simon Mukwembi, Henda C. Swart
- Discrete Mathematics
- 2011

If G is a connected graph with vertex set V , then the eccentric connectivity of G, Î¾ C (G), is defined as vâˆˆV deg(v) ec(v) where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. Weâ€¦ (More)

- Peter Dankelmann, Ivan Gutman, Simon Mukwembi, Henda C. Swart
- Discrete Applied Mathematics
- 2009

If G is a connected graph with vertex set V , then the degree distance of G, Dâ€²(G), is defined as âˆ‘ {u,v}âŠ†V (deg u + deg v) d(u, v), where deg w is the degree of vertex w, and d(u, v) denotes theâ€¦ (More)

- Patrick Ali, Simon Mukwembi, S. Munyira
- Discrete Applied Mathematics
- 2013

- Peter Dankelmann, Simon Mukwembi, Henda C. Swart
- Journal of Graph Theory
- 2009

The average distance Î¼(G) of a connected graph G of order n is the average of the distances between all pairs of vertices of G, i.e., Î¼(G) = ( n 2 )âˆ’1âˆ‘ {x,y}âŠ‚V (G) dG(x, y), where V (G) denotes theâ€¦ (More)

- Jaya Percival Mazorodze, Simon Mukwembi, TomÃ¡s VetrÃk
- Discrete Applied Mathematics
- 2014

- Patrick Ali, Peter Dankelmann, Simon Mukwembi
- Discrete Applied Mathematics
- 2012

Let G be a connected graph of order p and S a nonempty set of vertices of G. Then the Steiner distance d(S) of S is the minimum size of a connected subgraph of G whose vertex set contains S. If n isâ€¦ (More)

- Peter Dankelmann, David Erwin, Wayne Goddard, Simon Mukwembi, Henda C. Swart
- Australasian J. Combinatorics
- 2014

Let G be a connected graph. The eccentricity of a vertex v is defined as the distance in G between v and a vertex farthest from v. The nondecreasing sequence of the eccentricities of the vertices ofâ€¦ (More)