Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8901298 | Applied Mathematics and Computation | 2018 | 12 Pages |
Abstract
The resolvent energy ER(G) of a graph G on n vertices whose adjacency matrix has eigenvalues λ1,â¦,λn is the sum of the reciprocals of the numbers nâλ1,â¦,nâλn. We introduce 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Alexander Farrugia,