𝒫-energy of graphs
Given a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of 𝒫-eigenvalues of 𝒫-matrix of G. Apart from studying some properties of 𝒫-matrix, its eigenvalues and obtaining bounds of 𝒫-energy, we explore the robust(...
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Sciendo
2020-07-01
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| Series: | Acta Universitatis Sapientiae: Informatica |
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| Online Access: | https://doi.org/10.2478/ausi-2020-0009 |
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doaj-e7cbc9a884c04b99b9e91cbb2d0179df2021-09-06T19:41:25ZengSciendoActa Universitatis Sapientiae: Informatica2066-77602020-07-0112113715710.2478/ausi-2020-0009ausi-2020-0009𝒫-energy of graphsJoshi Prajakta Bharat0Joseph Mayamma1Department of Mathematics, CHRIST(Deemed to be University), Bangalore, India.Department of Mathematics, CHRIST(Deemed to be University), Bangalore,India.Given a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of 𝒫-eigenvalues of 𝒫-matrix of G. Apart from studying some properties of 𝒫-matrix, its eigenvalues and obtaining bounds of 𝒫-energy, we explore the robust(shear) 𝒫-energy which is the maximum(minimum) value of 𝒫-energy for some families of graphs. Further, we derive explicit formulas for E𝒫 (G) of few classes of graphs with different vertex partitions.https://doi.org/10.2478/ausi-2020-0009graph energyvertex partitionsk-partition matrixk-partition energy05c5005c69 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Joshi Prajakta Bharat Joseph Mayamma |
| spellingShingle |
Joshi Prajakta Bharat Joseph Mayamma 𝒫-energy of graphs Acta Universitatis Sapientiae: Informatica graph energy vertex partitions k-partition matrix k-partition energy 05c50 05c69 |
| author_facet |
Joshi Prajakta Bharat Joseph Mayamma |
| author_sort |
Joshi Prajakta Bharat |
| title |
𝒫-energy of graphs |
| title_short |
𝒫-energy of graphs |
| title_full |
𝒫-energy of graphs |
| title_fullStr |
𝒫-energy of graphs |
| title_full_unstemmed |
𝒫-energy of graphs |
| title_sort |
𝒫-energy of graphs |
| publisher |
Sciendo |
| series |
Acta Universitatis Sapientiae: Informatica |
| issn |
2066-7760 |
| publishDate |
2020-07-01 |
| description |
Given a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of 𝒫-eigenvalues of 𝒫-matrix of G. Apart from studying some properties of 𝒫-matrix, its eigenvalues and obtaining bounds of 𝒫-energy, we explore the robust(shear) 𝒫-energy which is the maximum(minimum) value of 𝒫-energy for some families of graphs. Further, we derive explicit formulas for E𝒫 (G) of few classes of graphs with different vertex partitions. |
| topic |
graph energy vertex partitions k-partition matrix k-partition energy 05c50 05c69 |
| url |
https://doi.org/10.2478/ausi-2020-0009 |
| work_keys_str_mv |
AT joshiprajaktabharat penergyofgraphs AT josephmayamma penergyofgraphs |
| _version_ |
1717766281352970240 |