Research articles
ScienceAsia 50 (2024):ID 2024009 16 doi:
10.2306/scienceasia15131874.2024.009
Existence and nonexistence of total eccentric graphical
intervals
Petchimuthu Manivannan^{a,*}, Mahilmaran Sundarakannan^{b}, Sonasalam Arockiaraj^{c}
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 ptotal 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 nonexistence 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, Email: manivannan.p10@gmail.com
Received 11 Apr 2022, Accepted 24 Aug 2023
