scholarly journals Bicyclic graphs with extremal values of PI index

2013 ◽  
Vol 161 (3) ◽  
pp. 395-403 ◽  
Author(s):  
Žana Kovijanić Vukićević ◽  
Dragan Stevanović
Keyword(s):  
Pi Index ◽  
Bicyclic Graphs ◽  
Extremal Values

scholarly journals On Mostar and Edge Mostar Indices of Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ali Ghalavand ◽  
Ali Reza Ashrafi ◽  
Mardjan Hakimi-Nezhaad
Keyword(s):  
Upper Bound ◽  
Graph Invariants ◽  
Open Questions ◽  
Bicyclic Graphs ◽  
Extremal Values

Let G be a graph with edge set E G and e = u v ∈ E G . Define n u e , G and m u e , G to be the number of vertices of G closer to u than to v and the number of edges of G closer to u than to v , respectively. The numbers n v e , G and m v e , G can be defined in an analogous way. The Mostar and edge Mostar indices of G are new graph invariants defined as M o G = ∑ u v ∈ E G n u u v , G − n v u v , G and M o e G = ∑ u v ∈ E G m u u v , G − m v u v , G , respectively. In this paper, an upper bound for the Mostar and edge Mostar indices of a tree in terms of its diameter is given. Next, the trees with the smallest and the largest Mostar and edge Mostar indices are also given. Finally, a recent conjecture of Liu, Song, Xiao, and Tang (2020) on bicyclic graphs with a given order, for which extremal values of the edge Mostar index are attained, will be proved. In addition, some new open questions are presented.

scholarly journals Extremal Values of Variable Sum Exdeg Index for Conjugated Bicyclic Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Muhammad Rizwan ◽  
Akhlaq Ahmad Bhatti ◽  
Muhammad Javaid ◽  
Ebenezer Bonyah
Keyword(s):  
Connected Graph ◽  
Perfect Matching ◽  
Matching Number ◽  
Bicyclic Graph ◽  
Bicyclic Graphs ◽  
Extremal Values

A connected graph G V , E in which the number of edges is one more than its number of vertices is called a bicyclic graph. A perfect matching of a graph is a matching in which every vertex of the graph is incident to exactly one edge of the matching set such that the number of vertices is two times its matching number. In this paper, we investigated maximum and minimum values of variable sum exdeg index, SEI a for bicyclic graphs with perfect matching for k ≥ 5 and a > 1 .

The weighted vertex PI index of bicyclic graphs

2018 ◽  
Vol 247 ◽  
pp. 309-321 ◽  
Author(s):  
Gang Ma ◽  
Qiuju Bian ◽  
Jianfeng Wang
Keyword(s):  
Pi Index ◽  
Weighted Vertex ◽  
Bicyclic Graphs

Extremal values of energy over oriented bicyclic graphs

2019 ◽  
Vol 342 ◽  
pp. 26-34 ◽  
Author(s):  
Juan Monsalve ◽  
Juan Rada ◽  
Yongtang Shi
Keyword(s):  
Bicyclic Graphs ◽  
Extremal Values

The maximum PI index of bicyclic graphs with even number of edges

2019 ◽  
Vol 146 ◽  
pp. 13-16
Author(s):  
Gang Ma ◽  
Qiuju Bian ◽  
Jianfeng Wang
Keyword(s):  
Pi Index ◽  
Bicyclic Graphs

scholarly journals Bounds on the PI index of unicyclic and bicyclic graphs with given girth

2017 ◽  
Vol 230 ◽  
pp. 156-161 ◽  
Author(s):  
Gang Ma ◽  
Qiuju Bian ◽  
Jianfeng Wang
Keyword(s):  
Pi Index ◽  
Bicyclic Graphs

Jahn-Teller Effect in Hexahydroxocuprate(II) Complexes

1995 ◽  
Vol 60 (9) ◽  
pp. 1429-1434
Author(s):  
Martin Breza
Keyword(s):  
Hydrogen Bonding ◽  
Quantum Chemical ◽  
Potential Surface ◽  
Hydroxyl Group ◽  
Chemical Calculation ◽  
Teller Distortion ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
Extremal Values ◽  
Jahn Teller Distortion

Using semiempirical CNDO-UHF method the adiabatic potential surface of 2[Cu(OH)6]4- complexes is investigated. The values of vibration and vibronic constants for Eg - (a1g + eg) vibronic interaction attain extremal values for the optimal O-H distance. The Jahn-Teller distortion decreases with increasing O-H distance. The discrepancy between experimentally observed elongated bipyramid of [Cu(OH)6]4- in Ba2[Cu(OH)6] and the compressed one obtained by quantum-chemical calculation is explainable by hydrogen bonding of the axial hydroxyl group.

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