20.500.12556/RUL-134930 Wiener complexity versus the eccentric complexity Let 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). graph diameter Wiener index transmission eccentricity graf diameter Winerjev indeks transmisija ekscentričnost true false true Angleški jezik Slovenski jezik Članek v reviji 2022-02-11 11:53:10 2022-02-11 11:53:11 2022-09-14 04:10:44 0000-00-00 00:00:00 2021 0 0 9 str. iss. 1, art. 79 Vol. 9 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 2227-7390 10.3390/math9010079 46211331 RAZ_Knor_Martin_2021.pdf RAZ_Knor_Martin_2021.pdf 1 3638354E474D803F3516197022EBE125 31f1aabd69388047975697d8e5c7a4b05910026428b5109fe118457795731865 df1265cd-8b28-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=153686 https://www.mdpi.com/2227-7390/9/1/79 0 b3ad517c-8b28-11ec-abdb-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=153685 Fakulteta za matematiko in fiziko 0 0 0