科研之友
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摘要
The conjecture Sigma(u is an element of V(G)) d(G)(u)(2)/n(G) <= Sigma(uv is an element of E(G))d(G)(u)d(G)(v)/m(G) that compares normalized Zagreb indices attracted recently a lot of attention(1-9). In this paper we analyze analogous statement in which degree d(G)(u) of vertex u is replaced by its eccentricity epsilon(G)(u) in which way we define novel first and second Zagreb eccentricity indices. We show that Sigma(u is an element of v(G)) epsilon(G)(u)(2)/n(G) >= Sigma(uv is an element of E(G)) epsilon(G)(u)epsilon(G)(v)/m(G) holds for all acyclic and unicyclic graphs and that neither this nor the opposite inequality holds for all bicyclic graphs.
- 出版日期2010
