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Title: | The increase in the resolvent energy of a graph due to the addition of a new edge |
Authors: | Farrugia, Alexander |
Keywords: | Graph theory -- Study and teaching (Higher) PI-algebras Polynomials Resolvents (Mathematics) |
Issue Date: | 2018 |
Publisher: | Elsevier |
Citation: | Farrugia, A. (2018). The increase in the resolvent energy of a graph due to the addition of a new edge. Applied Mathematics and Computation, 321, 25-36. |
Abstract: | The resolvent energy ER ( G ) of a graph G on n vertices whose adjacency matrix has eigen- values λ1 , . . . , λn is the sum of the reciprocals of the numbers n −λ1 , . . . , n −λn . We in troduce the resolvent energy matrix R ( G ) and present an algorithm that produces this matrix. This algorithm may also be used to update R ( G ) when new edges are introduced to G . Using the resolvent energy matrix R ( G ), we determine the increase in the resolvent energy ER ( G ) of G caused by such edge additions made to G . Moreover, we express this increase in terms of the characteristic polynomial of G and the characteristic polynomials of three vertex-deleted subgraphs of G . |
URI: | https://www.um.edu.mt/library/oar/handle/123456789/102145 |
Appears in Collections: | Scholarly Works - JCMath |
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