The energy of a graph

Balakrishnan, R.

doi:10.1016/j.laa.2004.02.038

Cited by 310 publications

(105 citation statements)

References 2 publications

Supporting

Mentioning

103

Contrasting

Unclassified

Order By: Relevance

“…Here we show inequality (1) also holds for SD(H). By direct calculation it can seen that the A-spectrum of H is {3.17741, 1.73205, 0.67836, 1 [2] , 1.73205, 1.85577}…”

Section: On Strong Graphs and Strong P-fold Graphsmentioning

confidence: 99%

“…[6n−10] , 3n+3 [5] , 3n+6 [2] , 3(n+3)± √ n 2 +6n−7 2 , 0}, with average vertex degree 3n − 1 + 6 n . We have .…”

Section: On Strong Graphs and Strong P-fold Graphsmentioning

confidence: 99%

“…This quantity, which is an extension of graph-energy concept has found remarkable chemical applications beyond the molecular orbital theory of conjugated molecules [20]. Both energy and Laplacian energy have been extensively studied in the literature (see [1,2,10,7,16,23,24,25] and the references therein). It is easy to see that tr(…”

Section: Introductionmentioning

confidence: 99%

“…So we have the following observation. Two graphs G 1 and G 2 of same order are said to be equienergetic if E(G 1 ) = E(G 2 ) see [2]. In analogy to this two graphs G 1 and G 2 of same order are said to L-equienergetic if LE(G 1 ) = LE(G 2 ) see [10,18,19].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On energy, Laplacian energy and p-fold graphs

Ganie

Pirzada

Baskoro

2015

ejgta

View full text Add to dashboard Cite

For a graph G having adjacency spectrum (A-spectrum) λ n ≤ λ n−1 ≤ · · · ≤ λ 1 and Laplacian spectrum (L-spectrum) 0 = µ n ≤ µ n−1 ≤ · · · ≤ µ 1 , the energy is defined as E(G) = n i=1 |λ i | and the Laplacian energy is defined as LE(G) = n i=1 |µ i − 2m n |. In this paper, we give upper and lower bounds for the energy of KK j n , 1 ≤ j ≤ n and as a consequence we generalize a result of Stevanovic et al. [22]. We also consider strong double graph and strong p-fold graph to construct some new families of graphs G for which E(G) > LE(G).

show abstract

“…Here we show inequality (1) also holds for SD(H). By direct calculation it can seen that the A-spectrum of H is {3.17741, 1.73205, 0.67836, 1 [2] , 1.73205, 1.85577}…”

Section: On Strong Graphs and Strong P-fold Graphsmentioning

confidence: 99%

“…[6n−10] , 3n+3 [5] , 3n+6 [2] , 3(n+3)± √ n 2 +6n−7 2 , 0}, with average vertex degree 3n − 1 + 6 n . We have .…”

Section: On Strong Graphs and Strong P-fold Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On energy, Laplacian energy and p-fold graphs

Ganie

Pirzada

Baskoro

2015

ejgta

View full text Add to dashboard Cite

show abstract

“…Estes grafos são chamados grafos simples, mas nos referiremos a eles como grafos. 4 , v 5 } e E = {e 1 , e 2 , e 3 , e 4 , e 5 , e 6 }, e portanto |V | = 5 e |E| = 6. As arestas são e 1 = {v 1 , v 2 }, e 2 = {v 2 , v 3 }, e 3 = {v 4 , v 5 }, e 4 = {v 1 , v 4 }, e 5 = {v 1 , v 5 } e e 6 = {v 2 Apresentamos a seguir alguns tipos especiais de grafos que aparecerão ao longo deste trabalho.…”

Section: Prefáciounclassified