Spectral Properties with the Difference between Topological Indices in Graphs
Let G be a graph of order n with vertices labeled as v1,v2,…,vn. Let di be the degree of the vertex vi, for i=1,2,…,n. The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero other...
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/6973078 |
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| author | Akbar Jahanbani Roslan Hasni Zhibin Du Seyed Mahmoud Sheikholeslami |
| author_facet | Akbar Jahanbani Roslan Hasni Zhibin Du Seyed Mahmoud Sheikholeslami |
| author_sort | Akbar Jahanbani |
| collection | DOAJ |
| description | Let G be a graph of order n with vertices labeled as v1,v2,…,vn. Let di be the degree of the vertex vi, for i=1,2,…,n. The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We also investigate the difference energy of a graph. In addition, we establish some upper and lower bounds for this new energy of graph. |
| format | Article |
| id | doaj-art-e503708f5a9143a9846fd913a6825d77 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e503708f5a9143a9846fd913a6825d772025-02-03T01:05:21ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/69730786973078Spectral Properties with the Difference between Topological Indices in GraphsAkbar Jahanbani0Roslan Hasni1Zhibin Du2Seyed Mahmoud Sheikholeslami3Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranFaculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, 21030 UMT, Kuala Nerus, Terengganu, MalaysiaSchool of Software, South China Normal University, Foshan, Guangdong 528225, ChinaDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranLet G be a graph of order n with vertices labeled as v1,v2,…,vn. Let di be the degree of the vertex vi, for i=1,2,…,n. The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We also investigate the difference energy of a graph. In addition, we establish some upper and lower bounds for this new energy of graph.http://dx.doi.org/10.1155/2020/6973078 |
| spellingShingle | Akbar Jahanbani Roslan Hasni Zhibin Du Seyed Mahmoud Sheikholeslami Spectral Properties with the Difference between Topological Indices in Graphs Journal of Mathematics |
| title | Spectral Properties with the Difference between Topological Indices in Graphs |
| title_full | Spectral Properties with the Difference between Topological Indices in Graphs |
| title_fullStr | Spectral Properties with the Difference between Topological Indices in Graphs |
| title_full_unstemmed | Spectral Properties with the Difference between Topological Indices in Graphs |
| title_short | Spectral Properties with the Difference between Topological Indices in Graphs |
| title_sort | spectral properties with the difference between topological indices in graphs |
| url | http://dx.doi.org/10.1155/2020/6973078 |
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