Stress-difference index for graphs. (English) Zbl 07905366
Summary: The stress of a vertex is a node centrality index, which has been introduced by A. Shimbel [Bull. Math. Biophys. 15, 501–507 (1953; doi:10.1007/BF02476438)]. The stress of a vertex in a graph is the number of geodesics (shortest paths) passing through it. A topological index of a chemical structure (graph) is a number that correlates the chemical structure with chemical reactivity or physical properties. In this paper, we introduce a new topological index for graphs called stress-difference index using stresses of vertices. Further, we establish some inequalities, prove some results and compute stress-difference index for some standard graphs. Also, we found that there is a positive correlation between the stress-difference index and some physical properties of lower alkanes.
MSC:
| 05Cxx | Graph theory |
Software:
CytoscapeReferences:
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