We improve hardness results for the problem of embedding one finite metric into another with minimum distortion. This problem is equivalent to optimally embedding one weighted graph into another under the shortest path metric. We show that unless P = NP, the minimum distortion of embedding one such graph into another cannot be efficiently approximated within a factor less than 9/4 even when the...

Soft set is a classification of elements the universe with respect to some given parameters. It new approach for modeling vagueness and uncertainty. The concept soft graph used provide parameterized point view graphs. In this paper we introduce concepts subdivision graph, power line investigate their properties.

The Gallai graph and the anti-Gallai graph of a graph G are edge disjoint spanning subgraphs of the line graph L(G). The vertices in the Gallai graph are adjacent if two of the end vertices of the corresponding edges in G coincide and the other two end vertices are nonadjacent in G. The anti-Gallai graph of G is the complement of its Gallai graph in L(G). Attributed to Gallai (1967), the study ...

This paper deals with the wavelength assignment problem in WDM all-optical networks. This problem can be abstracted as a multicoloring on a weighted conflict graph. The main focus of this work is to obtain the relationship between the wavelength assignment and the multicoloring problems. We, first, establish a new result regarding multicoloring problem in which we provide a tight bound for any ...

This paper represents a technique for finding optimal paths with multiple indexes in a graph. Up to the present time, all optimal paths have been determined upon one index, say, distance for which an evaluation method exists. In this paper firstly we define multiple indexes for each edge in such a way that anyone can treat the factor for assigning an optimal path. Here, we use Data Envelopment ...