On the Gutman index of Thorn graphs

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

10.22541/au.163820385.52737069/v1 ◽

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.

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Computation of Gutman index of some cactus chains

Electronic Journal of Graph Theory and Applications ◽

10.5614/ejgta.2018.6.1.10 ◽

2018 ◽

Vol 6 (1) ◽

pp. 138

Author(s):

Ali Sadeghieh ◽

Nima Ghanbari ◽

Saeid Alikhani

Keyword(s):

Gutman Index

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Weak and strong domination in thorn graphs

Asian-European Journal of Mathematics ◽

10.1142/s1793557120500710 ◽

2019 ◽

Vol 13 (04) ◽

pp. 2050071

Author(s):

Derya Doğan Durgun ◽

Berna Lökçü

Keyword(s):

Dominating Set ◽

Domination Number ◽

Minimum Cardinality ◽

Number Formula ◽

Thorn Graphs ◽

Domination Numbers

Let [Formula: see text] be a graph and [Formula: see text] A dominating set [Formula: see text] is a set of vertices such that each vertex of [Formula: see text] is either in [Formula: see text] or has at least one neighbor in [Formula: see text]. The minimum cardinality of such a set is called the domination number of [Formula: see text], [Formula: see text] [Formula: see text] strongly dominates [Formula: see text] and [Formula: see text] weakly dominates [Formula: see text] if (i) [Formula: see text] and (ii) [Formula: see text] A set [Formula: see text] is a strong-dominating set, shortly sd-set, (weak-dominating set, shortly wd-set) of [Formula: see text] if every vertex in [Formula: see text] is strongly (weakly) dominated by at least one vertex in [Formula: see text]. The strong (weak) domination number [Formula: see text] of [Formula: see text] is the minimum cardinality of an sd-set (wd-set). In this paper, we present weak and strong domination numbers of thorn graphs.

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

Discussiones Mathematicae Graph Theory ◽

10.7151/dmgt.1900 ◽

2016 ◽

Vol 36 (4) ◽

pp. 867

Author(s):

Jaya Percival Mazorodze ◽

Simon Mukwembi ◽

Tomáš Vetrik

Keyword(s):

Wiener Index ◽

Vertex Connectivity ◽

Gutman Index

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THE GUTMAN INDEX OF UNICYCLIC GRAPHS

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830912500310 ◽

2012 ◽

Vol 04 (03) ◽

pp. 1250031 ◽

Cited By ~ 1

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.

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