We compare two multicommodity ow problems, the maximum sum of ow, and the maximum concurrent ow. We show that, for a given graph and a given set of k commodities with speci ed demands, if the minimum capacity of a multicut is approximated by the maximum sum of ow within a factor of , for any subset of commodities, then the minimum cut ratio is approximated by the maximum concurrent ow within a ...

An asymptotic expansion is developed for the joint density of the sum and maximum of an i.i.d. sequence when the parent distribution is in the domain of extreme value attraction of the Gumbel distribution. Previous results by Chow and Teugels, extended by Anderson and Turkman, show that in this situation, the normalized sum and normalized maximum of the sample converge to independent normal and...

We introduce joins of signed graphs and explore the chromatic number all-positive all-negative joins. prove an analogue to theorem that join two equals sum their numbers. Given graphs, is usually less than numbers, by amount depends on new concept deficiency a signed-graph coloration.

The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...