NDLI: Remarks on Distance Based Topological Indices for ℓ-Apex Trees

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Remarks on Distance Based Topological Indices for ℓ-Apex Trees

Content Provider	MDPI
Author	Riste, Škrekovski Knor, Martin Imran, Muhammad Jamil, Muhammad Kamran
Copyright Year	2020
Description	A graph G is called an ℓ-apex tree if there exist a vertex subset $A\subsetV(G)$ with cardinality ℓ such that $G-A$ is a tree and there is no other subset of smaller cardinality with this property. In the paper, we investigate extremal values of several monotonic distance-based topological indices for this class of graphs, namely generalized Wiener index, and consequently for the Wiener index and the Harary index, and also for some newer indices as connective eccentricity index, generalized degree distance, and others. For the one extreme value we obtain that the extremal graph is a join of a tree and a clique. Regarding the other extreme value, which turns out to be a harder problem, we obtain results for $ℓ=1$ and pose some open questions for higher ℓ. Symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including topological indices of graphs.
Starting Page	802
e-ISSN	20738994
DOI	10.3390/sym12050802
Journal	Symmetry
Issue Number	5
Volume Number	12
Language	English
Publisher	MDPI
Publisher Date	2020-05-12
Access Restriction	Open
Subject Keyword	Symmetry Artificial Intelligence Apex Trees Distances in Apex Trees Generalized Wiener Index Extremal Graphs
Content Type	Text
Resource Type	Article

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