the index is excellent by the malmquist index as extended to productivity measurement. the index developed here is defined in terms of input cost rather than input quantity distance functions in supply chain. therefore, we propose productivity change is decomposed into overall efficiency and cost technical change. these decompositions provide a clearer situation of the root sources of supply ch...

wiener index is a topological index based on distance between every pair of vertices in agraph g. it was introduced in 1947 by one of the pioneer of this area e.g, harold wiener. inthe present paper, by using a new method introduced by klavžar we compute the wiener andszeged indices of some nanostar dendrimers.

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...

this paper deals with the basic notions of k-tautimmersions . these notions come from two special cases; that is, tight and taut immersions. tight and taut based on high and distance functions respectively and their basic notions are normal bundle, endpoint map, focal point, critical normal. we generalize hight and distance functions to cylindrical function and define basic notions of k-taut im...

This paper deals with the basic notions of k-tautimmersions . These notions come from two special cases; that is, tight and taut immersions. Tight and taut based on high and distance functions respectively and their basic notions are normal bundle, endpoint map, focal point, critical normal. We generalize hight and distance functions to cylindrical function and define basic notions of k-taut ...