Energy Conditions for Hamiltonicity of Graphs
Let G be an undirected simple graph of order n. Let A(G) be the adjacency matrix of G, and let μ1(G)≤μ2(G)≤⋯≤μn(G) be its eigenvalues. The energy of G is defined as ℰ(G)=∑i=1n|μi(G)|. Denote by GBPT a bipartite graph. In this paper, we establish the sufficient conditions for G having a Hamiltonian...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/305164 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549859606921216 |
|---|---|
| author | Guidong Yu Gaixiang Cai Miaolin Ye Jinde Cao |
| author_facet | Guidong Yu Gaixiang Cai Miaolin Ye Jinde Cao |
| author_sort | Guidong Yu |
| collection | DOAJ |
| description | Let G be an undirected simple graph of order n. Let A(G) be the adjacency matrix of G, and let μ1(G)≤μ2(G)≤⋯≤μn(G) be its eigenvalues. The energy of G is defined as ℰ(G)=∑i=1n|μi(G)|. Denote by GBPT a bipartite graph. In this paper, we establish the sufficient conditions for G having a Hamiltonian path or cycle or to be Hamilton-connected in terms of the energy of the complement of G, and give the sufficient condition for GBPT having a Hamiltonian cycle in terms of the energy of the quasi-complement of GBPT. |
| format | Article |
| id | doaj-art-70475ea4ecf44d2ebc42932a99100574 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-70475ea4ecf44d2ebc42932a991005742025-02-03T06:08:24ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/305164305164Energy Conditions for Hamiltonicity of GraphsGuidong Yu0Gaixiang Cai1Miaolin Ye2Jinde Cao3School of Mathematics & Computation Sciences, Anqing Normal College, Anqing 246011, ChinaSchool of Mathematics & Computation Sciences, Anqing Normal College, Anqing 246011, ChinaSchool of Mathematics & Computation Sciences, Anqing Normal College, Anqing 246011, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaLet G be an undirected simple graph of order n. Let A(G) be the adjacency matrix of G, and let μ1(G)≤μ2(G)≤⋯≤μn(G) be its eigenvalues. The energy of G is defined as ℰ(G)=∑i=1n|μi(G)|. Denote by GBPT a bipartite graph. In this paper, we establish the sufficient conditions for G having a Hamiltonian path or cycle or to be Hamilton-connected in terms of the energy of the complement of G, and give the sufficient condition for GBPT having a Hamiltonian cycle in terms of the energy of the quasi-complement of GBPT.http://dx.doi.org/10.1155/2014/305164 |
| spellingShingle | Guidong Yu Gaixiang Cai Miaolin Ye Jinde Cao Energy Conditions for Hamiltonicity of Graphs Discrete Dynamics in Nature and Society |
| title | Energy Conditions for Hamiltonicity of Graphs |
| title_full | Energy Conditions for Hamiltonicity of Graphs |
| title_fullStr | Energy Conditions for Hamiltonicity of Graphs |
| title_full_unstemmed | Energy Conditions for Hamiltonicity of Graphs |
| title_short | Energy Conditions for Hamiltonicity of Graphs |
| title_sort | energy conditions for hamiltonicity of graphs |
| url | http://dx.doi.org/10.1155/2014/305164 |
| work_keys_str_mv | AT guidongyu energyconditionsforhamiltonicityofgraphs AT gaixiangcai energyconditionsforhamiltonicityofgraphs AT miaolinye energyconditionsforhamiltonicityofgraphs AT jindecao energyconditionsforhamiltonicityofgraphs |