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• W3088354906 abstract "The eccentric connectivity polynomial (ECP) of a connected graph<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>V</mml:mi><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced><mml:mo>,</mml:mo><mml:mi>E</mml:mi><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:math>is described as<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:msup><mml:mrow><mml:mi>ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msup><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mstyle displaystyle=true><mml:msub><mml:mrow><mml:mo stretchy=false>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>a</mml:mi><mml:mo>∈</mml:mo><mml:mi>V</mml:mi><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msub><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=normal>deg</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mfenced><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>e</mml:mi><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:msup></mml:mrow></mml:mstyle></mml:math>, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi>e</mml:mi><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mfenced></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:msub><mml:mrow><mml:mi mathvariant=normal>deg</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:mfenced></mml:math>represent the eccentricity and the degree of the vertex<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>a</mml:mi></mml:math>, respectively. The eccentric connectivity index (ECI) can also be acquired from<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:msup><mml:mrow><mml:mi>ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msup><mml:mfenced open=( close=) separators=|><mml:mrow><mml:mi>G</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:mfenced></mml:math>by taking its first derivatives at<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>. The ECI has been widely used for analyzing both the boiling point and melting point for chemical compounds and medicinal drugs in QSPR/QSAR studies. As the extension of ECI, the ECP also performs a pivotal role in pharmaceutical science and chemical engineering. Graph products conveniently play an important role in many combinatorial applications, graph decompositions, pure mathematics, and applied mathematics. In this article, we work out the ECP of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mi mathvariant=normal>ℱ</mml:mi></mml:math>-sum of graphs. Moreover, we derive the explicit expressions of ECP for well-known graph products such as generalized hierarchical, cluster, and corona products of graphs. We also apply these outcomes to deduce the ECP of some classes of chemical graphs." @default.
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• W3088354906 title "On the Eccentric Connectivity Polynomial of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi mathvariant=normal>ℱ</mml:mi></mml:math>-Sum of Connected Graphs" @default.
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• W3088354906 doi "https://doi.org/10.1155/2020/5061682" @default.
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