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The Tutte Polynomial of Phenylene Systems with given number of branching hexagons
  • Hanlin Chen,
  • Chao Li
Hanlin Chen
National University of Defense Technology
Author Profile
Chao Li
National University of Defense Technology
Author Profile

Abstract

Polynomial graph invariants have been confirmed to have important applications in quantum chemistry and biological information. One of the famous polynomial graph invariants is the Tutte polynomial which gives multifarious interesting information about the graph structure. In this paper, we first give a simpler and more efficient method to get the Tutte polynomials of alternating polycyclic chains. Then we obtain the explicit expressions for the Tutte polynomials and the number of spanning trees of phenylene systems with given number of branching hexagons. Moreover, we determine the extremal values of the number of spanning trees among the phenylene systems with given one or two branching hexagons, and the corresponding extremal phenylene systems are characterized, respectively.
02 Mar 2022Submitted to International Journal of Quantum Chemistry
10 Mar 2022Submission Checks Completed
10 Mar 2022Assigned to Editor
15 Mar 2022Reviewer(s) Assigned
15 Mar 2022Review(s) Completed, Editorial Evaluation Pending
15 Mar 2022Editorial Decision: Revise Minor
26 Mar 20221st Revision Received
13 Apr 2022Submission Checks Completed
13 Apr 2022Assigned to Editor
14 Apr 2022Reviewer(s) Assigned
05 May 2022Review(s) Completed, Editorial Evaluation Pending
06 May 2022Editorial Decision: Revise Minor
10 May 20222nd Revision Received
11 May 2022Submission Checks Completed
11 May 2022Assigned to Editor
11 May 2022Reviewer(s) Assigned
11 May 2022Review(s) Completed, Editorial Evaluation Pending
11 May 2022Editorial Decision: Revise Minor
21 May 20223rd Revision Received
23 May 2022Assigned to Editor
23 May 2022Submission Checks Completed
25 May 2022Reviewer(s) Assigned
25 May 2022Review(s) Completed, Editorial Evaluation Pending
25 May 2022Editorial Decision: Accept