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ScienceAsia 50 (2024):ID 2024009 1-6 |doi: 10.2306/scienceasia1513-1874.2024.009


Existence and non-existence of total eccentric graphical intervals


Petchimuthu Manivannana,*, Mahilmaran Sundarakannanb, Sonasalam Arockiarajc

 
ABSTRACT:      A topological index is a numerical invariant which depicts the properties of molecules in accordance to their chemical structure. For a given integer n > 0, if a graph G exists with a total eccentric index of ?(G) = n, then ?n? is said to be total eccentric graphical, which is kind of an inverse problem for topological indices. An (integer) interval [?,?] is called p-total eccentric (free) interval if for all n ? [?,?] there exists a (no) graph G(p, q) with ?(G) = n. In this article, we determine several results for the existence and non-existence of total eccentric graphical intervals for graphs G on p vertices.

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a Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi, Tamil Nadu 626005 India
b Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai, Tamil Nadu 603110 India
c Department of Mathematics, Government Arts & Science College, Sivakasi, Tamil Nadu 626124 India

* Corresponding author, E-mail: manivannan.p10@gmail.com

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Received 11 Apr 2022, Accepted 24 Aug 2023