Some New Results on Various Graph Energies of the Splitting Graph

Chu, Zheng-Qing; Nazeer, Saima; Zia, Tariq Javed; Ahmed, Imran; Shahid, Sana

doi:10.1155/2019/7214047

Cited by 8 publications

(5 citation statements)

References 20 publications

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“…If m = 1 in Theorem 3.1, we get the Randić energy of splitting graph of G is ε R (Spl(G)) = 3 2 ε R (G) [7]. Corollary 3.2.…”

Section: Preliminariesmentioning

confidence: 95%

Energy and Randic' energy of special graphs

Jahfar¹,

Chithra²

2021

Preprint

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In this paper, we determine the Randić energy of the m-splitting graph, the m-shadow graph and the m-duplicate graph of a given graph, m being an arbitrary integer. Our results allow the construction of an infinite sequence of graphs having the same Randić energy. Further, we determine some graph invariants like the degree Kirchhoff index, the Kemeny's constant and the number of spanning trees of some special graphs. From our results, we indicate how to obtain infinitely many pairs of equienergetic graphs, Randić equienergetic graphs and also, infinite families of integral graphs.

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“…If m = 1 in Theorem 3.1, we get the Randić energy of splitting graph of G is ε R (Spl(G)) = 3 2 ε R (G) [7]. Corollary 3.2.…”

Section: Preliminariesmentioning

confidence: 95%

Energy and Randic' energy of special graphs

Jahfar¹,

Chithra²

2021

Preprint

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“…The Randic matrix is calculated as follows, r ij ( 5 ) d i and d j are the degrees of the vertices v i and v j respectively. The de nitions mentioned above were extracted from [2,5].…”

Section: De Nition 26mentioning

confidence: 99%

“…Randic Energy: This energy is de ned as the absolute sum of the eigenvalues of the Randic matrix. The Randic matrix is calculated as follows, r ij ( 5 ) d i and d j are the degrees of the vertices v i and v j respectively. The de nitions mentioned above were extracted from [2,5].…”

Section: De Nition 26mentioning

confidence: 99%

Application of Graph Energy in Glaucoma detection using Machine Learning Techniques

Hari¹,

Rajeshwar²,

Praba³

2023

Preprint

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Automatic detection of glaucoma from retinal fundus images is a major area of research in Computer aided diagnostics. In this paper, we propose a novel methodology to detect glaucoma by using energy of graph concepts. The retinal fundus image is first segmented to get the structure of the retinal vasculature using various image processing techniques. The retinal vasculature is then modeled into two graphs based on the position of branchpoints and the crossover points in the image. The graphs thus formed are simplified and 6 different energies are extracted from it. These energies are then used as features to a machine learning model i.e., quadratic support vector machine after performing principal component analysis. The methodology was tested out on the G1020 dataset and the results obtained show that energy of graphs does contain discriminating information regarding disease detection.

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“…Consider a finite, connected graph F ( γ ′ , δ ′ ) with β points and d edges. Let B =(b i j ) be the adjacency matrix of F. The various authors implemented their work in different dominations of graphs that were motivated by this (1)(2)(3) . So, we introduced the concept of a graph's minimum maximal dominating seidel energy.…”

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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Some New Results on Various Graph Energies of the Splitting Graph

Cited by 8 publications

References 20 publications

Energy and Randic' energy of special graphs

Energy and Randic' energy of special graphs

Application of Graph Energy in Glaucoma detection using Machine Learning Techniques

Some Standard Seidel Energy Results of the Minimum Maximal Dominating Graphs

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