Schultz and Modified Schultz Polynomials for Edge – Identification Chain and Ring – for Square Graphs

Ali, Ahmed M.; Abdullah, Mahmood M.

doi:10.21123/bsj.2022.19.3.0560

Cited by 4 publications

(5 citation statements)

References 9 publications

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“…There are a lot of papers that have been done to compute Schultz and modified Schultz polynomials and the indices for many graphs, for more information, see the references [6][7][8][9][10][11]. In this paper, we generalized the Schultz polynomial and modified the Schultz polynomial by taking all vertices degrees of the path, provided that the product of the length of the path with the sum of the degrees is a minimum, because of the importance of degrees as chemical bonds located on atoms and they are effects on the stability of the chemical compound.…”

Section: Najm and Alimentioning

confidence: 99%

Generalized Schultz and Modified Schultz Polynomials for Some Special Graphs

Najm,

Ali

2024

Iraqi Journal of Science

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With simple and undirected connected graph Φ, the Schultz and modified Schultz polynomials are defined as and , respectively, where the summation is taken over all unordered pairs of distinct vertices in V(Φ), where V(Φ) is the vertex set of Φ, degu is the degree of vertex u and d(v,u) is the ordinary distance between v and u, u≠v. In this study, the Shultz distance, modified Schultz distance, the polynomial, index, and average for both have been generalized, and this generalization has been applied to some special graphs.

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Section: Najm and Alimentioning

confidence: 99%

Generalized Schultz and Modified Schultz Polynomials for Some Special Graphs

Najm,

Ali

2024

Iraqi Journal of Science

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“…Note that throughout this study, we use the chromatic colourings of the graphs under consideration. Motivated by the studies on Schultz polynomial of graphs (see [1,2,4,5]), we can now introduce the chromatic version of the Schultz polynomial as follows:…”

Section: Chromatic Schultz Polynomial Of Graphsmentioning

confidence: 99%

“…The chromatic versions of certain topological indices have been introduced in [8]. The Schultz polynomials and modified Schultz polynomials of graphs are some of such widely studied polynomials (see [1,2,4]).…”

Section: Introductionmentioning

confidence: 99%

Chromatic Schultz polynomial of certain graphs

Naduvath

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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A topological index of a graph $G$ is a real number which is preserved under isomorphism. Extensive studies on certain polynomials related to these topological indices have also been done recently. In a similar way, chromatic versions of certain topological indices and the related polynomials have also been discussed in the recent literature. In this paper, the chromatic versions of the Schultz polynomial and modified chromatic Schultz polynomial are introduced and determined this polynomial for certain fundamental graph classes.

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“…Some standard seidel energy of domination in comprising transition metals of the bonds https://www.indjst.org/ between various elements reveals typical open-shell properties (7)(8)(9) . Such authors investigated their research in domination set of class of graph concepts such as metric dimension, domination set, edge-identification chain and ring can be developed in the concept of dominating sets in the paper (10,11) . This research investigates the prevailing of acyclic graphs and binomial graphs metric dimension of Corona product graphs (12)(13)(14) .…”

Section: Introductionmentioning

confidence: 99%

Some Standard Seidel Energy Results of the Minimum Maximal Dominating Graphs

Manthiram,

Annamalai

2024

IJST

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Objectives: Let be a finite and connected graph with β points and d edges. In this research, introduced the graph's minimum maximal dominating seidel energy ( and the properties of the latent roots of the given parameters are discussed. Method: In this research, the seidel energy of several graphs and its properties are investigated. Examined its minimum maximal limits and computed a few conventional seidel energy outcomes for the minimum maximal dominating graphs. Finding: Using the minimum maximal dominating seidel energy of graphs, significant outcomes were achieved for complete graphs, complete bipartite graphs, and star graphs. The properties of the class of graphs were computed. The established upper and lower bound is . Novelty: The seidel energy of the proposed research findings is used in various graphs based on the research. The fundamental characteristics of a graph, such as its energy upper and lower bounds, have been determined, and this knowledge has found notable chemical applications in the conjugated molecular orbital theory. Recommendations for future energy-related research are presented and examined. Keywords: Connected graph, Dominating set, Latent roots, Minimum maximal, Seidel energy

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Schultz and Modified Schultz Polynomials for Edge – Identification Chain and Ring – for Square Graphs

Cited by 4 publications

References 9 publications

Generalized Schultz and Modified Schultz Polynomials for Some Special Graphs

Generalized Schultz and Modified Schultz Polynomials for Some Special Graphs

Chromatic Schultz polynomial of certain graphs

Some Standard Seidel Energy Results of the Minimum Maximal Dominating Graphs

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