# Simon Mukwembi

• 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)
• 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)
• 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)
• 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)