Wiener complexity versus the eccentric complexityKnor, Martin (Avtor) Škrekovski, Riste (Avtor) graphdiameterWiener indextransmissioneccentricityLet w$_G$(u) be the sum of distances from u to all the other vertices of G. The Wiener complexity, C$_W$(G), is the number of different values of w$_G$(u) in G, and the eccentric complexity, C$_{ec}$(G), is the number of different eccentricities in G. In this paper, we prove that for every integer c there are infinitely many graphs G such that C$_W$(G) – C$_{ec}$(G) = c. Moreover, we prove this statement using graphs with the smallest possible cyclomatic number. That is, if c ≥ 0 we prove this statement using trees, and if c < 0 we prove it using unicyclic graphs. Further, we prove that C$_{ec}$(G) ≤ 2C$_W$(G) − 1 if G is a unicyclic graph. In our proofs we use that the function w$_G$(u) is convex on paths consisting of bridges. This property also promptly implies the already known bound for trees C$_{ec}$(G) ≤ C$_W$(G). Finally, we answer in positive an open question by finding infinitely many graphs G with diameter 3 such that C$_{ec}$(G) < C$_W$(G).20212022-02-11 11:53:10Članek v reviji134930UDK: 519.17ISSN pri članku: 2227-7390DOI: 10.3390/math9010079COBISS_ID: 46211331sl