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Relationship between the eccentric connectivity index and Zagreb indices
Computers and Mathematics With Applications, 2011 For a (molecular) graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices.
Kinkar Ch Das, Nenad Trinajstić
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On Connected Graphs Having the Maximum Connective Eccentricity Index
Journal of Applied Mathematics and Computing, 2021The connective eccentricity index (CEI) of a connected graph G is defined as $$\xi ^{ee}(G)=\sum _{u\in V_G}[d_G(u)/\varepsilon _G(u)]$$ , where $$d_G(u)$$ and
Shahid Zaman, Akbar Ali
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On Eccentric Connectivity Index and Connectivity
Acta Mathematica Sinica, English Series, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mukungunugwa, Vivian, Mukwembi, Simon
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On the Ediz eccentric connectivity index of a graph
, 2011 If G is a connected graph with vertex set V, then the Ediz eccentric connectivity index of G, (E)xi(c)(G), is defined as ()Sigma(v is an element of V) S(v)/ec(v) where S(v) is the sum of degrees of all vertices adjacent to vertex v and ec(v) is its eccentricity.
Ediz, Süleyman
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Inverse connective eccentricity index and its applications
2021Summary: The inverse connective eccentricity index of a connected graph \(G\) is defined as \(\xi^{-1}_{ce}(G) = \sum\limits_{u\in V(G)}\frac{\epsilon_G(u)}{d_G(u)}\), where \(\epsilon_G(u)\) and \(d_G(u)\) are the eccentricity and degree of a vertex \(u\) in \(G\), respectively.
Pattabiraman, K, Suganya, T
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Eccentric connectivity index in complementary prisms
Discrete Mathematics, Algorithms and ApplicationsThe topological index is just one of several very useful tools that graph theory has made available to chemists. Topological indices are invariants of real numbers under graph isomorphisms. Several topological indices have been defined. Some of them are used to model chemical, pharmaceutical and other properties of molecules.
Aytac, Aysun, Coskun, Belgin
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On the maximum connective eccentricity index among k-connected graphs
Discrete Mathematics, Algorithms and Applications, 2020The connective eccentricity index (CEI for short) of a graph [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the degree of [Formula: see text] and [Formula: see text] is the eccentricity of [Formula: see text] in [Formula: see text].
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Eccentric connectivity index: extremal graphs and values
2010Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially
DOŠLIĆ, T. +2 more
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Connective eccentric index of fullerenes
2011Fullerenes are carbon-cage molecules in which a number of carbon atoms are bonded in a nearly spherical configuration. The connective eccentric index of graph G is defined as C (G)= Σa V(G)deg(a)e(a) -1, where e(a) is defined as the length of a maximal path connecting a to another vertex of G.
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The augmented eccentric connectivity index of nanotubes and nanotori
2012Let G be a connected graph, the augmented eccentric connectivity index is a topological index was defined as $zeta(G)=sum_{i=1}^nM_i/E_i$, where Mi is the product of degrees of all vertices vj, adjacent to vertex vi, Ei is the largest distance between vi and any other vertex vk of G or the eccentricity of i v and n is the number of vertices in graph G.
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