STRESS INDICES OF GRAPHS
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The stress of a vertex in a graph had been introduced by Shimbel in 1953 as the number of geodesics (shortest paths) passing through it. A topological index of a chemical structure (molecular graph) is a number that correlates given chemical structure with a chemical reactivity or physical property. In this paper, we introduce two new topological indices for graphs called rst and second stress indices by means of the notion of stress of a vertex. Further, we establish some inequalities, prove some fundamental results and compute these stress indices for some standard graphs. These two indices are expected to give new applications in chemistry and social science problems as the notion of stress of a vertex depends on the geodesics passing through that vertex and may lead to new notions related to graphs.
Abstract
The stress of a vertex in a graph had been introduced by Shimbel in 1953 as the number of geodesics (shortest paths) passing through it. A topological index of a chemical structure (molecular graph) is a number that correlates given chemical structure with a chemical reactivity or physical property. In this paper, we introduce two new topological indices for graphs called rst and second stress indices by means of the notion of stress of a vertex. Further, we establish some inequalities, prove some fundamental results and compute these stress indices for some standard graphs. These two indices are expected to give new applications in chemistry and social science problems as the notion of stress of a vertex depends on the geodesics passing through that vertex and may lead to new notions related to graphs.
참고문헌 (7)
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- A. Shimbel, "Structural Parameters of Communication Networks", Bulletin of Mathe-matical Biophysics, 15, pp.501~507 (1953)