A review on eigen values of adjacency matrix of graph with cliques

Carnia, Ema; Suyudi, Moch.; Aisah, Isah; Supriatna, Asep K.

doi:10.1063/1.4995116

Cited by 6 publications

(4 citation statements)

References 26 publications

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“…Let all the elements in G be self-inverse elements. By Definition 1, Γ(G) is a complete graph of order n and the spectra of K n is given by [4] as…”

Section: Further Results On Non-inverse Graphsmentioning

confidence: 99%

On the non-inverse graph of a group

Amreen¹,

Naduvath²

2022

Discuss. Math. - General Algebra and Applications

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Let (G, * ) be a finite group and S = {u ∈ G|u = u −1 }, then the inverse graph is defined as a graph whose vertices coincide with G such that two distinct vertices u and v are adjacent if and only if either u * v ∈ S or v * u ∈ S. In this paper, we introduce a modified version of the inverse graph, called i * -graph associated with a group G. The i * -graph is a simple graph with vertex set consisting of elements of G and two vertices x, y ∈ Γ are adjacent if x and y are not inverses of each other. We study certain properties and characteristics of this graph. Some parameters of the i *graph are also determined.

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“…Let all the elements in G be self-inverse elements. By Definition 1, Γ(G) is a complete graph of order n and the spectra of K n is given by [4] as…”

Section: Further Results On Non-inverse Graphsmentioning

confidence: 99%

On the non-inverse graph of a group

Amreen¹,

Naduvath²

2022

Discuss. Math. - General Algebra and Applications

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“…The adjacency matrix 𝐴 of 𝐺, with respect to this listing of the vertices, is the 𝑛 × 𝑛 zero one matrix with 1 as its (𝑖, 𝑗)𝑡ℎ entry when 𝑣 𝑖 and 𝑣 𝑗 are adjacent, and 0 as its (𝑖, 𝑗)𝑡ℎ entry when they are not adjacent [14]. However, in this study, the entry of the adjacency matrix is the weight of edge from vertex 𝑖 to vertex 𝑗.…”

Section: Determining the Adjacency Matrix For The Sentence Graph And ...mentioning

confidence: 99%

Changing Active to Passive Sentence in Indonesian using Graph Theory and Pascal

Bahri,

Firdaus

2024

Mal. J. Fund. Appl. Sci.

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This study discusses how graph theory is employed to changes four types of active sentence patterns into passive sentences in Indonesian. By considering 12 types of words as vertices, a weighted active sentence graph is constructed. The graph is then converted into an adjacency matrix. Furthermore, by using the transformation, the adjacency matrix is converted into a passive sentence adjacency matrix. The adjacency matrix is converted back into a passive sentence graph. From this graph, a passive sentence is generated. In the end, the Pascal program for converting active sentence to passive sentence is also used.

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“…The adjacency matrix of a 2 n -cycle graph can be deduced following the pattern presented in [35], as shown in Eq. (12).…”

Section: Dtqw On the N-cycle Graphmentioning

confidence: 99%

Circuit implementation of discrete-time quantum walks via the shunt decomposition method

Wing-Bocanegra

Venegas-Andraca

2023

Quantum Inf Process

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Several models have been proposed to build evolution operators to perform quantum walks in a theoretical way, although when wanting to map the resulting evolution operators into quantum circuits to run them in quantum computers, it is often the case that the mapping process is in fact complicated. Nevertheless, when the adjacency matrix of a graph can be decomposed into a sum of permutation matrices, we can always build a shift operator for a quantum walk that has a block diagonal matrix representation. In this paper, we analyze the mapping process of block diagonal operators into quantum circuit form, and apply this method to obtain quantum circuits that generate quantum walks on the most common topologies found in the literature: the straight line, the cyclic graph, the hypercube and the complete graph. The obtained circuits are then executed on quantum processors of the type Falcon r5.11L and Falcon r4T (two of each type) through IBM Quantum Composer platform and on the Qiskit Aer simulator, performing three steps for each topology. The resulting distributions were compared against analytical distributions, using the statistical distance 1 as a performance metric. Regarding experimental executions, we obtained short 1 distances in the cases of quantum circuits with a low amount of multi-control gates, being the quantum processors of the type Falcon r4T the ones that provided more accurate results.

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A review on eigen values of adjacency matrix of graph with cliques

Cited by 6 publications

References 26 publications

On the non-inverse graph of a group

On the non-inverse graph of a group

Changing Active to Passive Sentence in Indonesian using Graph Theory and Pascal

Circuit implementation of discrete-time quantum walks via the shunt decomposition method

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