On the relation between Wiener index and eccentricity of a graph
نویسندگان
چکیده
The relation between the Wiener index W(G) and eccentricity $$\varepsilon (G)$$ of a graph G is studied. Lower upper bounds on in terms are proved extremal graphs characterized. A Nordhaus–Gaddum type result involving given. sharp bound tree its proved. It shown that class trees same order, difference $$W(T) - \varepsilon (T)$$ minimized caterpillars. An exact formula for radius T obtained. lower also Two conjectures proposed. first asserts $$W(G) does not increase after contracting an edge G. second conjecture largest paths.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2021
ISSN: ['1573-2886', '1382-6905']
DOI: https://doi.org/10.1007/s10878-021-00724-2