Bounds for graph energy in terms of vertex covering and clique numbers

Samee, U.; Pirzada, S.; Ganie, Hilal A.

doi:10.5614/ejgta.2019.7.2.9

Cited by 6 publications

(3 citation statements)

References 20 publications

(23 reference statements)

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“…The minimum size of a vertex cover is denoted by β(Γ). Our other used notations about graphs are standard and for more details one may see [6,7,11].…”

Section: Introductionmentioning

confidence: 99%

Some structural graph properties of the non-commuting graph of a class of finite Moufang loops

Bashir

Ahmadidelir

2020

EJGTA

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For any non-abelian group G, the non-commuting graph of G, Γ = Γ G , is graph with vertex set G\Z(G), where Z(G) is the set of elements of G that commute with every element of G and distinct non-central elements x and y of G are joined by an edge if and only if xy = yx. The non-commuting graph of a finite Moufang loop has been defined by Ahmadidelir. In this paper, we show that the multiple complete split-like graphs and the non-commuting graph of Chein loops of the form M (D 2n , 2) are perfect (but not chordal). Then, we show that the non-commuting graph of a non-abelian group G is split if and only if the non-commuting graph of the Moufang loop M (G, 2) is 3−split. Precisely, we show that the non-commuting graph of the Moufang loop M (G, 2), is 3−split if and only if G is isomorphic to a Frobenius group of order 2n, n is odd, whose Frobenius kernel is abelian of order n. Finally, we calculate the energy of generalized and multiple splite-like graphs, and discuss about the energy and also the number of spanning trees in the case of the non-commuting graph of Chein loops of the form M (D 2n , 2).

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“…The minimum size of a vertex cover is denoted by β(Γ). Our other used notations about graphs are standard and for more details one may see [6,7,11].…”

Section: Introductionmentioning

confidence: 99%

Some structural graph properties of the non-commuting graph of a class of finite Moufang loops

Bashir

Ahmadidelir

2020

EJGTA

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“…Until now, hundreds of such "energy" have been introduced, such as inverse sum index energy [6], distance energy [7,8], ABC energy [9,10], matching energy [11,12], and Randić energy [13,14]. Recently, there are many studies, such as [15][16][17], on the energy of graphs with given parameters.…”

Section: Introductionmentioning

confidence: 99%

Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

Wang

Gao

2020

Mathematical Problems in Engineering

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Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

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“…From this work, other energies associated with graphs emerged, such as incidence energy [19] in 2009 and signless Laplacian energy [17] in 2010. Additionally, new developments in the study of (adjacency) graph energy, may be seen in, for example, [12,25].…”

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confidence: 99%

Energies of Hypergraphs

Cardoso

Trevisan

2020

ELA

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In this paper, energies associated with hypergraphs are studied. More precisely, results are obtained for the incidence and the singless Laplacian energies of uniform hypergraphs. In particular, bounds for the incidence energy are obtained as functions of well known parameters, such as maximum degree, Zagreb index and spectral radius. It is also related the incidence and signless Laplacian energies of a hypergraph with the adjacency energies of its subdivision graph and line multigraph, respectively. In addition, the signless Laplacian energy for the class of the power hypergraphs is computed.

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Bounds for graph energy in terms of vertex covering and clique numbers

Cited by 6 publications

References 20 publications

Some structural graph properties of the non-commuting graph of a class of finite Moufang loops

Some structural graph properties of the non-commuting graph of a class of finite Moufang loops

Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

Energies of Hypergraphs

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