Relationship between the Hosoya polynomial and the hyper-Wiener index

✍ Scribed by G.G. Cash

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 256 KB
• Volume: 15
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(02)00059-9

✦ Synopsis

The Hosoya polynomial of a graph, H(G, z), has the property that its first derivative, evaluated at z = 1, equals the Wiener index, i.e

., W(G) = H'(G, 1). In this paper, an equation is presented that gives the hyper-Wiener index, WW(G), in terms of the first and second derivatives of H(G,z).

Also defined here is a hyper-Hosoya polynomial, HH(G,r), which has the property WW(G) = HH'(G, l), analogous to W(G) = H'(G, 1). Uses of higher derivatives of HH(G,z)

are proposed, analogous to published uses of higher derivatives of H(G, 2).