Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
On the Palindromic Hosoya Polynomial of Trees. / Badulin, Dmitry; Grebennikov, Alexandr; Vorob'ev, Konstantin.
в: Match, Том 88, № 2, 2022, стр. 471-478.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On the Palindromic Hosoya Polynomial of Trees
AU - Badulin, Dmitry
AU - Grebennikov, Alexandr
AU - Vorob'ev, Konstantin
N1 - Publisher Copyright: © 2022 University of Kragujevac, Faculty of Science. All rights reserved.
PY - 2022
Y1 - 2022
N2 - A graph G on n vertices of diameter D is called H-palindromic if d(G, k) = d(G,D - k) for all k = 0, 1, . . . , [D 2 ] , where d(G, k) is the number of unordered pairs of vertices at distance k. Quantities d(G, k) form coefficients of the Hosoya polynomial. In 1999, Caporossi, Dobrynin, Gutman and Hansen found five H-palindromic trees of even diameter and conjectured that there are no such trees of odd diameter. We prove this conjecture for bipartite graphs. An infinite family of H-palindromic trees of diameter 6 is also constructed.
AB - A graph G on n vertices of diameter D is called H-palindromic if d(G, k) = d(G,D - k) for all k = 0, 1, . . . , [D 2 ] , where d(G, k) is the number of unordered pairs of vertices at distance k. Quantities d(G, k) form coefficients of the Hosoya polynomial. In 1999, Caporossi, Dobrynin, Gutman and Hansen found five H-palindromic trees of even diameter and conjectured that there are no such trees of odd diameter. We prove this conjecture for bipartite graphs. An infinite family of H-palindromic trees of diameter 6 is also constructed.
UR - http://www.scopus.com/inward/record.url?scp=85129639318&partnerID=8YFLogxK
U2 - 10.46793/match.88-2.471B
DO - 10.46793/match.88-2.471B
M3 - Article
AN - SCOPUS:85129639318
VL - 88
SP - 471
EP - 478
JO - Match
JF - Match
SN - 0340-6253
IS - 2
ER -
ID: 98340648