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Subgraphs of pair vertices. (English) Zbl 1171.05433

Summary: Subgraphs obtained by applying several fragmentation criteria are investigated. Two well known criteria (Szeged and Cluj), and two new others are defined and characterized. An example is given for the discussed procedures. The matrix and polynomial representations of vertices composing each type of subgraphs were also given. Analytical formulas for the polynomials of several classes of graphs are derived. The newly introduced subgraphs/fragments, called MaxF and CMaxF, appear to have interesting properties, which are demonstrated.

MSC:

05C90 Applications of graph theory
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
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References:

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