scholarly journals Computation of Gutman index of some cactus chains

2018 ◽  
Vol 6 (1) ◽  
pp. 138
Author(s):  
Ali Sadeghieh ◽  
Nima Ghanbari ◽  
Saeid Alikhani
Keyword(s):  
Gutman Index

scholarly journals The expected values for the Gutman index, Schultz index, multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index of a random cyclooctatetraene chain

2021 ◽  
Author(s):  
Xianya Geng ◽  
Jinfeng Qi ◽  
Minjie Zhang
Keyword(s):  
Kirchhoff Index ◽  
Schultz Index ◽  
Expected Values ◽  
Gutman Index ◽  
Analytical Expressions

In this paper, we mainly solve the explicit analytical expressions for the expected values of the Gutman index, Schultz index, multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index of a random cyclooctatetraene chain with $n$ octagons. We also obtain the average values of these four indices with respect to the set of all these cyclooctatetraene chains.

scholarly journals The Gutman index and the edge-Wiener index of graphs with given vertex-connectivity

2016 ◽  
Vol 36 (4) ◽  
pp. 867
Author(s):  
Jaya Percival Mazorodze ◽  
Simon Mukwembi ◽  
Tomáš Vetrik
Keyword(s):  
Wiener Index ◽  
Vertex Connectivity ◽  
Gutman Index

THE GUTMAN INDEX OF UNICYCLIC GRAPHS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250031 ◽  
Author(s):  
LIHUA FENG
Keyword(s):  
Connected Graph ◽  
Unicyclic Graphs ◽  
Degree Of Vertex ◽  
Vertex Set ◽  
Gutman Index

Let G be a connected graph with vertex set V(G). The Gutman index of G is defined as S(G) = ∑{u, v}⊆V(G) d(u)d(v)d(u, v), where d(u) is the degree of vertex u, and d(u, v) denotes the distance between u and v. In this paper, we characterize n-vertex unicyclic graphs with girth k, having minimal Gutman index.

Distance-based indices of complete m-ary trees

2020 ◽  
Vol 12 (04) ◽  
pp. 2050041
Author(s):  
Mesfin Masre ◽  
Samuel Asefa Fufa ◽  
Tomáš Vetrík
Keyword(s):  
Computer Science ◽  
Recurrence Relations ◽  
Wiener Index ◽  
The Other ◽  
Binary Trees ◽  
New Methods ◽  
Degree Distance ◽  
Gutman Index ◽  
Eccentric Distance

Binary and [Formula: see text]-ary trees have extensive applications, particularly in computer science and chemistry. We present exact values of all important distance-based indices for complete [Formula: see text]-ary trees. We solve recurrence relations to obtain the value of the most well-known index called the Wiener index. New methods are used to express the other indices (the degree distance, the eccentric distance sum, the Gutman index, the edge-Wiener index, the hyper-Wiener index and the edge-hyper-Wiener index) as well. Values of distance-based indices for complete binary trees are corollaries of the main results.

scholarly journals Computing Exact Values for Gutman Indices of Sum Graphs under Cartesian Product

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Abdulaziz Mohammed Alanazi ◽  
Faiz Farid ◽  
Muhammad Javaid ◽  
Augustine Munagi
Keyword(s):  
Connected Graph ◽  
Topological Index ◽  
Cartesian Product ◽  
Chemical Compounds ◽  
Factor Graphs ◽  
Cartesian Products ◽  
Degree Distance ◽  
Gutman Index ◽  
Extremal Theory ◽  
Theory Of Graphs

Gutman index of a connected graph is a degree-distance-based topological index. In extremal theory of graphs, there is great interest in computing such indices because of their importance in correlating the properties of several chemical compounds. In this paper, we compute the exact formulae of the Gutman indices for the four sum graphs (S-sum, R-sum, Q-sum, and T-sum) in the terms of various indices of their factor graphs, where sum graphs are obtained under the subdivision operations and Cartesian products of graphs. We also provide specific examples of our results and draw a comparison with previously known bounds for the four sum graphs.

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