On Subtree Number Index of Generalized Book Graphs, Fan Graphs, and Wheel Graphs

Sun, Daoqiang; Zhao, Zhengying; Li, Xiaoxiao; Jun, Cao; Yu, Yang

doi:10.1155/2021/5511214

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…These wheel networks are useful in networking and communication, as every node is one hoop neighbor to another. In 2021, Daoqiang et al [20] studied the subtree number index of wheel graphs and other types of graphs. In 2022, Kuswardi et al [21] investigated the chromatic number of the amalgamation of wheel graphs.…”

Section: Literature Review Of Studies Of Wheel Graphsmentioning

confidence: 99%

On Laplacian Eigenvalues of Wheel Graphs

Alotaibi,

Alghamdi,

Alolaiyan

2023

Symmetry

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Consider G to be a simple graph with n vertices and m edges, and L(G) to be a Laplacian matrix with Laplacian eigenvalues of μ1,μ2,…,μn=zero. Write Sk(G)=∑i=1kμi as the sum of the k-largest Laplacian eigenvalues of G, where k∈{1,2,…,n}. The motivation of this study is to solve a conjecture in algebraic graph theory for a special type of graph called a wheel graph. Brouwer’s conjecture states that Sk(G)≤m+k+12, where k=1,2,…,n. This paper proves Brouwer’s conjecture for wheel graphs. It also provides an upper bound for the sum of the largest Laplacian eigenvalues for the wheel graph Wn+1, which provides a better approximation for this upper bound using Brouwer’s conjecture and the Grone–Merris–Bai inequality. We study the symmetry of wheel graphs and recall an example of the symmetry group of Wn+1, n≥3. We obtain our results using majorization methods and illustrate our findings in tables, diagrams, and curves.

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Section: Literature Review Of Studies Of Wheel Graphsmentioning

confidence: 99%

On Laplacian Eigenvalues of Wheel Graphs

Alotaibi,

Alghamdi,

Alolaiyan

2023

Symmetry

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“…In (9) the spectral properties of varoius types of graphs were discussed and the spectrum for some were also determined. In (10) the sub-tree generating functions and the sub-tree number index of generalized book graphs, generalized fan graphs, and generalized wheel graphs were determined.In this article, we determined the CD-number for the k th power of PVB-tree and ((OT r ) k ) where 2 ≤ k ≤ 7.…”

Section: Introductionmentioning

confidence: 99%

Generalization of CD-Number for Power Graph of Some Special Types of Tree Graphs

Praveenkumar,

Mahadevan,

Sivagnanam

2024

IJST

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Objectives: The main objective of the article is to finding the corona domination for the power graph of some special types of tree graph. Method: A dominating set of a graph is said to be a corona dominating set if every vertex in is either a pendant vertex or a support vertex. The minimum cardinality of a corona dominating set is called the corona domination number and is denoted by . Findings: In this article, we study the -number for the power of PVB-tree and where and identify their exact values. Novelty: The corona domination was one of the recently developed domination parameter, along with this parameter we found the exact value for some special types of graphs. Keywords: Domination Number, Corona Domination Number, Total Domination, Power Graphs, Olive Tree And PVBTree

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“…Book graph is formed by multiple C 3 sharing an edge. Fan graph is the corona product of K 1 and P n (10) . Section 2, determines the exact γ TCC values of the certain graphs by increasing the distance between the vertices of the considered graph and generalized the results for power graph of some special graphs.…”

Section: Introductionmentioning

confidence: 99%

Generalizing TCCD-Number For Power Graph Of Some Graphs

Kaviya,

Mahadevan,

Sivagnanam

2024

IJST

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Objective: Finding the triple connected certified domination number for the power graph of some peculiar graphs. Methods: A dominating set with the condition that every vertex in has either zero or at least two neighbors in and is triple connected is a called triple connected certified domination number of a graph. The minimum cardinality among all the triple connected certified dominating sets is called the triple connected certified domination number and is denoted by . The upper bound and lower bound of for the given graphs is found and then proved the upper bound and lower bound of were equal. Findings: We found the (TCCD)-number for the power graph of some peculiar graphs. Also, we have generalized the result for path, cycle, ladder graph, comb graph, coconut tree graph, triangular snake, alternate triangular snake, quadrilateral snake and tadpole graph. Novelty: The triple connected certified domination is a new parameter in which the certified domination holds the triple connected in induced . Keywords: Domination Number, Power Graphs, Triple Connected, Certified Domination, Triple Connected Certified Domination

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On Subtree Number Index of Generalized Book Graphs, Fan Graphs, and Wheel Graphs

Cited by 3 publications

References 26 publications

On Laplacian Eigenvalues of Wheel Graphs

On Laplacian Eigenvalues of Wheel Graphs

Generalization of CD-Number for Power Graph of Some Special Types of Tree Graphs

Generalizing TCCD-Number For Power Graph Of Some Graphs

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