Minimum eccentric connectivity index for graphs with fixed order and fixed number of pendant vertices
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. We characterize, with a new elegant proof, those graphs which have the smallest...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Belgrade
2019-01-01
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| Series: | Yugoslav Journal of Operations Research |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/0354-0243/2019/0354-02431900010D.pdf |
| Summary: | 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. We characterize, with a new elegant proof, those graphs which have the smallest eccentric connectivity index among all connected graphs of a given order n. Then, 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. |
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| ISSN: | 0354-0243 1820-743X |