Inverse problem for Bell index

Togan, Muge; Yurttas, Aysun; Sanli, Utkum; Celik, Feriha; Cangual, Ismail

doi:10.2298/fil2002615t

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…. , 15 e second hyper-Zagreb index of a tree (or molecular) graph can be any positive integer, except 2, 3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,28,29,30,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,57,59,60,61,62,63,65,66,…”

Section: E Ip For Second Hyper-zagreb Indexmentioning

confidence: 99%

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On the Inverse Problem for Some Topological Indices

Maji

Ghorai

Mahmood

et al. 2021

Journal of Mathematics

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The study of the inverse problem (IP) based on the topological indices (TIs) deals with the numerical relations to TIs. Mathematically, the IP can be expressed as follows: given a graph parameter/TI that assigns a non-negative integer value g to every graph within a given family G of graphs, find some G ∈ G for which TI G = g . It was initiated by the Zefirov group in Moscow and later Gutman et al. proposed it. In this paper, we have established the IP only for the Y -index, Gourava indices, second hyper-Zagreb index, reformulated first Zagreb index, and reformulated F -index since they are closely related to each other. We have also studied the same which is true for the molecular, tree, unicyclic, and bicyclic graphs.

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Section: E Ip For Second Hyper-zagreb Indexmentioning

confidence: 99%

“…In [26], Czabarka et al solved the IP for certain tree parameters. To study more about the inverse problems and the topological indices of graph operations, one can see these references [27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

On the Inverse Problem for Some Topological Indices

Maji

Ghorai

Mahmood

et al. 2021

Journal of Mathematics

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On the σt-irregularity and the inverse irregularity problem

Dimitrov¹,

Stevanović

2023

Applied Mathematics and Computation

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On the inverse Collatz-Sinogowitz irregularity problem

2023

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The Collatz-Sinogowitz irregularity index is the oldest known numerical measure of graph irregularity. For a simple and connected graph G G of order n n and size m m , it is defined as CS ( G ) = λ 1 − 2 m / n , \hspace{0.1em}\text{CS}\hspace{0.1em}\left(G)={\lambda }_{1}-2m\hspace{0.1em}\text{/}\hspace{0.1em}n, where λ 1 {\lambda }_{1} is the largest eigenvalue of the adjacency matrix of G G , and 2 m / n 2m\hspace{0.1em}\text{/}\hspace{0.1em}n is the average vertex degree of G G . Here, the Collatz-Sinogowitz inverse irregularity problem is studied. For every integer i ≥ 0 i\ge 0 , it is shown that there exists a graph G G such that CS ( G ) = i \hspace{0.1em}\text{CS}\hspace{0.1em}\left(G)=i . Also, for every interval I i = ( i , i + 1 ) {I}_{i}=\left(i,i+1) , it is shown that there are infinitely many graphs whose Collatz-Sinogowitz irregularity lies in I i {I}_{i} .

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Inverse problem for Bell index

Cited by 3 publications

References 9 publications

On the Inverse Problem for Some Topological Indices

On the Inverse Problem for Some Topological Indices

On the σt-irregularity and the inverse irregularity problem

On the inverse Collatz-Sinogowitz irregularity problem

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