On the variable sum exdeg index/coindex of graphs

Ali, A. Mohamed; Milovanovic, Emina I.; Matejic, Marjan; Milovanovic, Igor Z.

doi:10.46793/match.87-1.133a

Cited by 9 publications

(10 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, d n , we define e r (G) = n i=1 d r i . This is a well-studied graph parameter, especially in chemical graph theory, see the survey [1]. There the quantity n i=1 d α i is called the general zeroth order Randic index, but the names first general Zagreb index and variable first Zagreb index are also used in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…There the quantity n i=1 d α i is called the general zeroth order Randic index, but the names first general Zagreb index and variable first Zagreb index are also used in the literature. Section 2.4 of the survey [1] deals with the maximum value of this index among n-vertex F -free graphs. This line of research was initiated by Caro and Yuster [6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Note on Stability for Maximal F-Free Graphs

Gerbner

2021

Graphs and Combinatorics

View full text Add to dashboard Cite

Popielarz, Sahasrabuddhe and Snyder in 2018 proved that maximal $$K_{r+1}$$ K r + 1 -free graphs with $$(1-\frac{1}{r})\frac{n^2}{2}-o(n^{\frac{r+1}{r}})$$ ( 1 - 1 r ) n 2 2 - o ( n r + 1 r ) edges contain a complete r-partite subgraph on $$n-o(n)$$ n - o ( n ) vertices. This was very recently extended to odd cycles in place of $$K_3$$ K 3 by Wang, Wang, Yang and Yuan. We further extend it to some other 3-chromatic graphs, and obtain some other stability results along the way.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Note on Stability for Maximal F-Free Graphs

Gerbner

2021

Graphs and Combinatorics

View full text Add to dashboard Cite

show abstract

“…During the study of molecular structures [18], the second Zagreb index appeared; they are denoted by M 1 and M 2 respectively. In [19][20][21][22], these indices have been widely discussed and investigated.…”

Section: Introductionmentioning

confidence: 99%

Zagreb connection topological descriptors and structural property of the triangular chain structures

Ullah¹,

udin²,

Zaman³

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

Mathematical chemistry is concerned with the use of mathematics to solve the problems in chemistry. A triangular chain graph is a simple graph composed of a series of triangles. This chain is widely used in the formation of triangular cactus, boron clusters, boron triangular nanotubes, and boron nanotubes. In this paper, the first Zagreb connection index, the first modified Zagreb connection index, and the second Zagreb connection index for triangular chain structures are calculated and derived closed formulas for them. Based on the derived formulas and obtained numerical results, the physicochemical properties of these type of structures can easily be investigated.

show abstract

“…In [19], some exact formulations and bounds were presented in terms of topological indices, particularly the first Zagreb index, few inequalities for Zagreb index were computed in [20], some other results on the topological indices were found in [21][22][23]. Neighborhood first Zagreb index was introduced and its some properties were discussed in [24].…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach for Extremal General Exponential Multiplicative Zagreb Indices

Ismail

Azeem

Shang

et al. 2023

Axioms

View full text Add to dashboard Cite

The study of the maximum and minimal characteristics of graphs is the focus of the significant field of mathematics known as extreme graph theory. Finding the biggest or smallest graphs that meet specified criteria is the main goal of this discipline. There are several applications of extremal graph theory in various fields, including computer science, physics, and chemistry. Some of the important applications include: Computer networking, social networking, chemistry and physics as well. Recently, in 2021 exponential multiplicative Zagreb indices were introduced. In generalization, we introduce the generalized form of exponential multiplicative Zagreb indices for α∈R+\{1}. Furthermore, to see the behaviour of generalized first and second exponential Zagreb indices for α∈R+\{1}, we used a transformation method. In term of the two newly developed generalized exponential multiplicative Zagreb indices, we will investigate the extremal bicyclic, uni-cyclic and trees graphs. Four graph transformations are used and some bounds are presented in terms of generalized exponential multiplicative Zagreb indices.

show abstract

On the variable sum exdeg index/coindex of graphs

Cited by 9 publications

References 12 publications

A Note on Stability for Maximal F-Free Graphs

A Note on Stability for Maximal F-Free Graphs

Zagreb connection topological descriptors and structural property of the triangular chain structures

A Unified Approach for Extremal General Exponential Multiplicative Zagreb Indices

Contact Info

Product

Resources

About