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- Title
MINIMUM ECCENTRIC CONNECTIVITY INDEX FOR GRAPHS WITH FIXED ORDER AND FIXED NUMBER OF PENDANT VERTICES.
- Authors
DEVILLEZ, Gauvain; HERTZ, Alain; MÉLOT, Hadrien; HAUWEELE, Pierre
- Abstract
The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product dG(v)eG(v), where dG(v) is the degree of v in G and eG(v) is the maximum distance between v and any other vertex of G. This index is helpful for the prediction of biological activities of diverse nature, a molecule being modeled as a graph where atoms are represented by vertices and chemical bonds by edges. We characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of a given order n. Also, given two integers n and p with p≤n-1, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order n with p pendant vertices.
- Subjects
MOLECULAR connectivity index; GRAPH connectivity; CHEMICAL bonds; GEOMETRIC vertices; MOLECULAR models; GRAPH theory
- Publication
Yugoslav Journal of Operations Research, 2019, Vol 29, Issue 2, p193
- ISSN
0354-0243
- Publication type
Article
- DOI
10.2298/YJOR181115010D