Croatica Chemica Acta, Vol. 89 No. 4, 2016.
Original scientific paper
https://doi.org/10.5562/cca3036
Chemistry-Relevant Isospectral Graphs. Acyclic Conjugated Polyenes
Haruo Hosoya
; Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan
Abstract
By using the topological index Z and Z-counting polynomial proposed by the present author isospectral (IS) pairs of acyclic conjugated polyenes (C2nH2n+2) were studied. Besides the hitherto known smallest pair of n = 6, four and twenty seven pairs of n = 7 and 8, respectively, were first reported. Inspection of these results revealed several new features of IS tree graphs, i.e., appearance of two pairs of endospectral vertices in a tree graph and existence of several families of IS pair graphs whose Z-indices systematically grow up to infinity. Further several IS pairs were found to be closely related with each other topologically and called “intrinsic” IS pairs. Important role of the Z-index for analyzing the IS graphs is demonstrated.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Keywords
isospectral tree graph; cospectral tree graph; acyclic conjugated polyene; topological index Z; Z-index; graph theory
Hrčak ID:
180733
URI
Publication date:
19.12.2016.
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