On Randić energy

Gutman, Iván; Furtula, Boris; Bozkurt, Ş. Burcu

doi:10.1016/j.laa.2013.06.010

Cited by 82 publications

(64 citation statements)

References 15 publications

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“…38 A recently discovered unexpected mathematical feature of the Randić index is its connection with the normalized Laplacian matrix. [39][40][41] …”

Section: Randić or Connectivity Indexmentioning

confidence: 99%

Degree-Based Topological Indices

Gutman¹

2013

Croat. Chem. Acta

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637

384

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“…38 A recently discovered unexpected mathematical feature of the Randić index is its connection with the normalized Laplacian matrix. [39][40][41] …”

Section: Randić or Connectivity Indexmentioning

confidence: 99%

Degree-Based Topological Indices

Gutman¹

2013

Croat. Chem. Acta

Self Cite

637

384

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“…Gutman et al [14] pointed out that the Randić-index-concept is purposeful to associate the graph G a symmetric square matrix of order n, named Randić matrix R(G) = (r ij ), where…”

Section: Introductionmentioning

confidence: 99%

“…. , n. Some basic properties of the Randić index, Randić matrix and Randić energy were determined in the papers [3,4,5,6,10,11,12,14,17,22,23,24,29].…”

Section: Introductionmentioning

confidence: 99%

Hermitian-Randić matrix and Hermitian-Randić energy of mixed graphs

Wang

Zhou

2017

J Inequal Appl

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Let M be a mixed graph and be its Hermitian-adjacency matrix. If we add a Randić weight to every edge and arc in M, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix of a mixed graph M, where () if is an arc of M, if is an undirected edge of M, and otherwise. In this paper, firstly, we compute the characteristic polynomial of the Hermitian-Randić matrix of a mixed graph. Furthermore, we give bounds on the Hermitian-Randić energy of a general mixed graph. Finally, we give some results about the Hermitian-Randić energy of mixed trees.

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“…The work by Gutman [22] signposted a fruitful relationship between graph energy and various eigenvalues of matrices associated to graphs. This leads to a wealth of work on energy-like graph spectral invariant in regards to, e.g., (signless) Laplacian matrix [27,28], Randić matrix [29], and distance matrix [30]. More recent results can be found in [17,18,24,[29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

On the Generalized Distance Energy of Graphs

2019

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is the distance matrix and Tr(G) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α (G). Some new upper and lower bounds for the generalized distance energy E D α (G) of G are established based on parameters including the Wiener index W(G) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

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On Randić energy

Cited by 82 publications

References 15 publications

Degree-Based Topological Indices

Degree-Based Topological Indices

Hermitian-Randić matrix and Hermitian-Randić energy of mixed graphs

On the Generalized Distance Energy of Graphs

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