Discrete Applied Mathematics
Note: Upper bounds on the Steiner diameter of a graph
Discrete Applied Mathematics
On the extremal properties of the average eccentricity
Computers & Mathematics with Applications
| Hi-index | 0.00 |
The average distance μ(G) of a connected graphG of order n is the average of the distances betweenall pairs of vertices of G, i.e., μ(G) = (n2)-1Σ{x,y}‚V(G)dG(x, y), where V(G) denotesthe vertex set of G and dG(x, y) isthe distance between x and y. We prove that everyconnected graph of order n and minimum degree δ has aspanning tree T with average distance at most $${n\over\delta + 1} + 5$$. We give improved bounds forK3-free graphs, C4-free graphs,and for graphs of given girth. © 2000 John Wiley & Sons,Inc. J Graph Theory 33: 113, 2000