| Summary: | The connective eccentricity index (CEI) of a hypergraph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula> is defined as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>ξ</mi><mrow><mi>c</mi><mi>e</mi></mrow></msup><mrow><mo>(</mo><mi mathvariant="script">G</mi><mo>)</mo></mrow><mo>=</mo><msub><mo>∑</mo><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi mathvariant="script">G</mi><mo>)</mo></mrow></msub><mfrac><mrow><msub><mi>d</mi><mi mathvariant="script">G</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow><mrow><msub><mi>ε</mi><mi mathvariant="script">G</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></mfrac></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ε</mi><mi mathvariant="script">G</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mi mathvariant="script">G</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> denote the eccentricity and the degree of the vertex <i>v</i>, respectively. In this paper, we determine the maximal and minimal values of the connective eccentricity index among all <i>k</i>-uniform hypertrees on <i>n</i> vertices and characterize the corresponding extremal hypertrees. Finally, we establish some relationships between the connective eccentricity index and the eccentric connectivity index of hypergraphs.
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