scholarly journals On the general sum-connectivity index of connected unicyclic graphs with k pendant vertices

2015 ◽  
Vol 181 ◽  
pp. 306-309 ◽  
Author(s):  
Ioan Tomescu ◽  
Misbah Arshad
Keyword(s):  
Connectivity Index ◽  
Unicyclic Graphs

General eccentric connectivity index of trees and unicyclic graphs

2020 ◽  
Vol 284 ◽  
pp. 301-315
Author(s):  
Tomáš Vetrík ◽  
Mesfin Masre
Keyword(s):  
Connectivity Index ◽  
Eccentric Connectivity Index ◽  
Unicyclic Graphs

General sum-connectivity index of unicyclic graphs with given diameter and girth

2021 ◽  
pp. 2150140
Author(s):  
Tomáš Vetrík
Keyword(s):  
Lower Bounds ◽  
Topological Indices ◽  
Connectivity Index ◽  
Index Formula ◽  
Extremal Graphs ◽  
Unicyclic Graphs ◽  
Harmonic Index

Topological indices of graphs have been studied due to their extensive applications in chemistry. We obtain lower bounds on the general sum-connectivity index [Formula: see text] for unicyclic graphs [Formula: see text] of given girth and diameter, and for unicyclic graphs of given diameter, where [Formula: see text]. We present the extremal graphs for all the bounds. Our results generalize previously known results on the harmonic index for unicyclic graphs of given diameter.

Minimum general sum-connectivity index of unicyclic graphs

2010 ◽  
Vol 48 (3) ◽  
pp. 697-703 ◽  
Author(s):  
Zhibin Du ◽  
Bo Zhou ◽  
Nenad Trinajstić
Keyword(s):  
Connectivity Index ◽  
Unicyclic Graphs

scholarly journals Sharp Lower Bounds of the Sum-Connectivity Index of Unicyclic Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Maryam Atapour
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Connectivity Index ◽  
Unicyclic Graphs ◽  
Sharp Lower Bound

The sum-connectivity index of a graph G is defined as the sum of weights 1 / d u + d v over all edges u v of G , where d u and d v are the degrees of the vertices u and v in graph G , respectively. In this paper, we give a sharp lower bound on the sum-connectivity index unicyclic graphs of order n ≥ 7 and diameter D G ≥ 5 .

The eccentric adjacency index of unicyclic graphs and trees

2018 ◽  
Vol 13 (01) ◽  
pp. 2050028 ◽  
Author(s):  
Shehnaz Akhter ◽  
Rashid Farooq
Keyword(s):  
Connected Graph ◽  
Connectivity Index ◽  
Eccentric Connectivity Index ◽  
Unicyclic Graphs ◽  
Vertex Set ◽  
Simple Connected Graph ◽  
Eccentric Adjacency Index

Let [Formula: see text] be a simple connected graph with vertex set [Formula: see text] and edge set [Formula: see text]. The eccentricity [Formula: see text] of a vertex [Formula: see text] in [Formula: see text] is the largest distance between [Formula: see text] and any other vertex of [Formula: see text]. The eccentric adjacency index (also known as Ediz eccentric connectivity index) of [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the sum of degrees of neighbors of the vertex [Formula: see text]. In this paper, we determine the unicyclic graphs with largest eccentric adjacency index among all [Formula: see text]-vertex unicyclic graphs with a given girth. In addition, we find the tree with largest eccentric adjacency index among all the [Formula: see text]-vertex trees with a fixed diameter.

scholarly journals On the eccentric connectivity coindex in graphs

2021 ◽  
Vol 7 (1) ◽  
pp. 651-666
Author(s):  
Hongzhuan Wang ◽  
◽  
Xianhao Shi ◽  
Ber-Lin Yu
Keyword(s):  
Lower Bounds ◽  
Connected Graph ◽  
Topological Index ◽  
Extremal Problems ◽  
Connectivity Index ◽  
Adjacent Vertex ◽  
Extremal Graph ◽  
Eccentric Connectivity Index ◽  
Unicyclic Graphs

<abstract><p>The well-studied eccentric connectivity index directly consider the contribution of all edges in a graph. By considering the total eccentricity sum of all non-adjacent vertex, Hua et al. proposed a new topological index, namely, eccentric connectivity coindex of a connected graph. The eccentric connectivity coindex of a connected graph $ G $ is defined as</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \overline{\xi}^{c}(G) = \sum\limits_{uv\notin E(G)} (\varepsilon_{G}(u)+\varepsilon_{G}(v)). $\end{document} </tex-math></disp-formula></p> <p>Where $ \varepsilon_{G}(u) $ (resp. $ \varepsilon_{G}(v) $) is the eccentricity of the vertex $ u $ (resp. $ v $). In this paper, some extremal problems on the $ \overline{\xi}^{c} $ of graphs with given parameters are considered. We present the sharp lower bounds on $ \overline{\xi}^{c} $ for general connecteds graphs. We determine the smallest eccentric connectivity coindex of cacti of given order and cycles. Also, we characterize the graph with minimum and maximum eccentric connectivity coindex among all the trees with given order and diameter. Additionally, we determine the smallest eccentric connectivity coindex of unicyclic graphs with given order and diameter and the corresponding extremal graph is characterized as well.</p></abstract>

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