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- W2037744281 abstract "The resistance distance<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:msub><mml:mrow><mml:mi>Ω</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false>(</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>between vertices<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:math>of a connected (molecular) graph<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>is computed as the effective resistance between nodes<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:math>in the corresponding network constructed from<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>by replacing each edge of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>with a unit resistor. The conductance excess between any<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:math>of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M11><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>is the difference between<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M12><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>Ω</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=false>(</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>and the reciprocal of the distance between<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M13><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M14><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:math>. The global cyclicity index of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M15><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:math>is defined as the sum of conductance excesses between all pairs of adjacent vertices. In this paper, by computing resistance distances between pairs of adjacent vertices in linear polyacenes, an explicit formula for the global cyclicity index of a benzenoid chain is obtained in terms of its number of hexagons." @default.
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- W2037744281 date "2013-01-01" @default.
- W2037744281 modified "2023-10-17" @default.
- W2037744281 title "The Global Cyclicity Index of Benzenoid Chains" @default.
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