메뉴 건너뛰기




Volumn 432, Issue 9, 2010, Pages 2257-2272

Towards a spectral theory of graphs based on the signless Laplacian, II

Author keywords

Adjacency matrix; Graph spectra; Graph theory; Laplacian; Signless Laplacian

Indexed keywords

ADJACENCY MATRICES; BIPARTITE GRAPHS; COMMON FEATURES; COSPECTRAL GRAPHS; EIGENVALUES; GRAPH SPECTRA; INTEGRAL GRAPHS; LAPLACIANS; LINE GRAPH; M-THEORY; MATRIX; REGULAR GRAPHS; SPANNING TREE; SPECTRAL GRAPH THEORY; SPECTRAL THEORY;

EID: 77149151598     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2009.05.020     Document Type: Article
Times cited : (224)

References (48)
  • 1
    • 77149163766 scopus 로고    scopus 로고
    • Some notes on the threshold graphs
    • in press
    • M. Andjelić, S.K. Simić, Some notes on the threshold graphs, in press.
    • Andjelić, M.1    Simić, S.K.2
  • 2
    • 77149124848 scopus 로고    scopus 로고
    • K. Balińska, D. Cvetković, Z. Radosavljević, S. Simić, D. Stevanović, A survey on integral graphs, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat. 13 (2002) 42-65 (Errata, These Publications 15 (2004) 112).
    • K. Balińska, D. Cvetković, Z. Radosavljević, S. Simić, D. Stevanović, A survey on integral graphs, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat. 13 (2002) 42-65 (Errata, These Publications 15 (2004) 112).
  • 4
    • 52449128742 scopus 로고    scopus 로고
    • A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph
    • Cardoso D., Cvetković D., Rowlinson P., and Simić S. A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph. Linear Algebra Appl. 429 (2008) 2770-2780
    • (2008) Linear Algebra Appl. , vol.429 , pp. 2770-2780
    • Cardoso, D.1    Cvetković, D.2    Rowlinson, P.3    Simić, S.4
  • 7
    • 0141707483 scopus 로고
    • Root systems, forbidden subgraphs and spectral characterizations of line graphs
    • D. Cvetković, I. Gutman, T. Pisanski, R. Tošić Eds, April 15-16, University of Novi Sad, Institute of Mathematics, Novi Sad
    • D. Cvetković, M. Doob, Root systems, forbidden subgraphs and spectral characterizations of line graphs, in: D. Cvetković, I. Gutman, T. Pisanski, R. Tošić (Eds.), Graph Theory, Proc. Fourth Yugoslav. Sem. Graph Theory, Novi Sad, April 15-16, 1983, University of Novi Sad, Institute of Mathematics, Novi Sad, 1984, pp. 69-99.
    • (1983) Graph Theory, Proc. Fourth Yugoslav. Sem. Graph Theory, Novi Sad , pp. 69-99
    • Cvetković, D.1    Doob, M.2
  • 8
    • 0004092833 scopus 로고
    • third ed, Johann Ambrosius Barth Verlag, Heidelberg, Leipzig
    • D. Cvetković, M. Doob, H. Sachs, Spectra of Graphs, third ed., Johann Ambrosius Barth Verlag, Heidelberg, Leipzig, 1995.
    • (1995) Spectra of Graphs
    • Cvetković, D.1    Doob, M.2    Sachs, H.3
  • 9
    • 0442304561 scopus 로고
    • On the spectral structure of graphs having the maximal eigenvalue not greater than two
    • Cvetković D., and Gutman I. On the spectral structure of graphs having the maximal eigenvalue not greater than two. Publ. Inst. Math. (Beograd) 18 32 (1975) 39-45
    • (1975) Publ. Inst. Math. (Beograd) , vol.18 , Issue.32 , pp. 39-45
    • Cvetković, D.1    Gutman, I.2
  • 14
    • 67649235867 scopus 로고    scopus 로고
    • Towards a spectral theory of graphs based on signless Laplacian I
    • Cvetković D., and Simić S.K. Towards a spectral theory of graphs based on signless Laplacian I. Publ. Inst. Math. (Beograd) 85 99 (2009) 19-33
    • (2009) Publ. Inst. Math. (Beograd) , vol.85 , Issue.99 , pp. 19-33
    • Cvetković, D.1    Simić, S.K.2
  • 15
    • 0141607701 scopus 로고    scopus 로고
    • Which graphs are determined by their spectrum?
    • van Dam E.R., and Haemers W. Which graphs are determined by their spectrum?. Linear Algebra Appl. 373 (2003) 241-272
    • (2003) Linear Algebra Appl. , vol.373 , pp. 241-272
    • van Dam, E.R.1    Haemers, W.2
  • 16
    • 59649130014 scopus 로고    scopus 로고
    • Developments on spectral characterization of graphs, Discrete Math
    • doi:10.1016/jdisc.2008.08.019
    • E.R. van Dam, W. Haemers, Developments on spectral characterization of graphs, Discrete Math., CentER Discussion Paper 2007-33, 2007, pp, 1-17, doi:10.1016/jdisc.2008.08.019.
    • (2007) CentER Discussion Paper , vol.2007 -33 , pp. 1-17
    • van Dam, E.R.1    Haemers, W.2
  • 18
    • 45749140063 scopus 로고    scopus 로고
    • Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs
    • Fan Y.-Z., Tam B.-S., and Zhou J. Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs. Linear and Multilinear Algebra 56 4 (2008) 381-397
    • (2008) Linear and Multilinear Algebra , vol.56 , Issue.4 , pp. 381-397
    • Fan, Y.-Z.1    Tam, B.-S.2    Zhou, J.3
  • 19
    • 33750856785 scopus 로고    scopus 로고
    • Minimizing the Laplacian spectral radius of trees with given matching number
    • Feng L., Li Q., and Zhang X.-D. Minimizing the Laplacian spectral radius of trees with given matching number. Linear and Multilinear Algebra 55 2 (2007) 199-207
    • (2007) Linear and Multilinear Algebra , vol.55 , Issue.2 , pp. 199-207
    • Feng, L.1    Li, Q.2    Zhang, X.-D.3
  • 21
    • 77149121699 scopus 로고    scopus 로고
    • The signless Laplacian spectral radius of unicyclic graphs with graph constraints
    • Feng L., and Yu G. The signless Laplacian spectral radius of unicyclic graphs with graph constraints. Kyungpook Math. 49 (2009) 123-131
    • (2009) Kyungpook Math. , vol.49 , pp. 123-131
    • Feng, L.1    Yu, G.2
  • 22
    • 67649145529 scopus 로고    scopus 로고
    • The signless Laplacian spectral radius of graphs with given diameter
    • in press
    • L.-H. Feng, G.-H. Yu, The signless Laplacian spectral radius of graphs with given diameter, Utilitas Math., in press.
    • Utilitas Math
    • Feng, L.-H.1    Yu, G.-H.2
  • 23
    • 67649232804 scopus 로고    scopus 로고
    • On three conjectures involving the signless Laplacian spectral radius of graphs
    • L.-H. Feng, G.-H. Yu, On three conjectures involving the signless Laplacian spectral radius of graphs, Publ. Inst. Math. (Beograd) 85(99) 35-38.
    • Publ. Inst. Math. (Beograd) , vol.85 , Issue.99 , pp. 35-38
    • Feng, L.-H.1    Yu, G.-H.2
  • 25
    • 2442640405 scopus 로고
    • On the spectral radii of topologically equivalent graphs
    • M. Fiedler Ed, Academia Praha
    • A.J. Hoffman, J.H. Smith, On the spectral radii of topologically equivalent graphs, in: M. Fiedler (Ed.), Recent Advances in Graph Theory, Academia Praha, 1975, pp. 273-281.
    • (1975) Recent Advances in Graph Theory , pp. 273-281
    • Hoffman, A.J.1    Smith, J.H.2
  • 26
    • 0006796947 scopus 로고
    • On the largest eigenvalue of graphs (Chinese)
    • Li Q., and Feng K.E. On the largest eigenvalue of graphs (Chinese). Acta Math. Appl. Sinica 2 (1979) 167-175
    • (1979) Acta Math. Appl. Sinica , vol.2 , pp. 167-175
    • Li, Q.1    Feng, K.E.2
  • 27
    • 58049163607 scopus 로고    scopus 로고
    • The maximum clique and the signless Laplacian eigenvalues
    • Liu J., and Liu B. The maximum clique and the signless Laplacian eigenvalues. Czechoslovak Math. J. 58 4 (2008) 1233-1240
    • (2008) Czechoslovak Math. J. , vol.58 , Issue.4 , pp. 1233-1240
    • Liu, J.1    Liu, B.2
  • 28
    • 0001633258 scopus 로고
    • On the spectral characterization of trees
    • B.D. McKay, On the spectral characterization of trees, Ars Combin. 3 (1977) 219-232.
    • (1977) Ars Combin , vol.3 , pp. 219-232
    • McKay, B.D.1
  • 29
    • 33750999449 scopus 로고
    • Laplacian matrices of graphs: a survey
    • Merris R. Laplacian matrices of graphs: a survey. Linear Algebra Appl. 197-198 (1994) 143-176
    • (1994) Linear Algebra Appl. , vol.197-198 , pp. 143-176
    • Merris, R.1
  • 30
    • 77149122360 scopus 로고    scopus 로고
    • C.S. Oliveira, L.S. Lima, N.M.M. de, Abreu, P. de, Hansen, Bounds on the index of the signless Laplacian of a graph, Les Cahiers du GERAD, G-2007-72.
    • C.S. Oliveira, L.S. Lima, N.M.M. de, Abreu, P. de, Hansen, Bounds on the index of the signless Laplacian of a graph, Les Cahiers du GERAD, G-2007-72.
  • 32
    • 33847273846 scopus 로고    scopus 로고
    • Starlike trees are determined by their Laplacian spectrum
    • Omidi G.R., and Tajbakhsh K. Starlike trees are determined by their Laplacian spectrum. Linear Algebra Appl. 422 (2007) 654-658
    • (2007) Linear Algebra Appl. , vol.422 , pp. 654-658
    • Omidi, G.R.1    Tajbakhsh, K.2
  • 33
    • 2442636601 scopus 로고
    • On the largest eigenvalue of bicyclic graphs
    • Simić S.K. On the largest eigenvalue of bicyclic graphs. Publ. Math. Inst. (Beograd) 46 60 (1989) 1-6
    • (1989) Publ. Math. Inst. (Beograd) , vol.46 , Issue.60 , pp. 1-6
    • Simić, S.K.1
  • 34
    • 34249335247 scopus 로고
    • On the largest eigenvalue of some homeomorphic graphs
    • Simić S.K., and Kocić V.Lj. On the largest eigenvalue of some homeomorphic graphs. Publ. Inst. Math. (Beograd) 40 54 (1986) 3-9
    • (1986) Publ. Inst. Math. (Beograd) , vol.40 , Issue.54 , pp. 3-9
    • Simić, S.K.1    Kocić, V.Lj.2
  • 35
    • 48549085290 scopus 로고    scopus 로고
    • Q-integral graphs with edge-degrees at most five
    • Simić S.K., and Stanić Z. Q-integral graphs with edge-degrees at most five. Discrete Math. 308 (2008) 4625-4634
    • (2008) Discrete Math. , vol.308 , pp. 4625-4634
    • Simić, S.K.1    Stanić, Z.2
  • 36
    • 65749119954 scopus 로고    scopus 로고
    • On some forests determined by their Laplacian or signless Laplacian spectrum
    • in press, doi:10.1016/j.camwa.2009.04.005
    • S.K. Simić, Z. Stanić, On some forests determined by their Laplacian or signless Laplacian spectrum, Comput. Math. Appl., in press, doi:10.1016/j.camwa.2009.04.005.
    • Comput. Math. Appl
    • Simić, S.K.1    Stanić, Z.2
  • 38
    • 77149134902 scopus 로고    scopus 로고
    • Z. Stanić, Some reconstructions in spectral graph theory and Q-integral graphs, (Serbian), Doctoral Thesis, Faculty of Mathematics, Belgrade, 2007.
    • Z. Stanić, Some reconstructions in spectral graph theory and Q-integral graphs, (Serbian), Doctoral Thesis, Faculty of Mathematics, Belgrade, 2007.
  • 39
    • 60749092827 scopus 로고    scopus 로고
    • There are exactly 172 connected Q-integral graphs up to 10 vertices
    • Stanić Z. There are exactly 172 connected Q-integral graphs up to 10 vertices. Novi Sad J. Math. 37 2 (2007) 193-205
    • (2007) Novi Sad J. Math. , vol.37 , Issue.2 , pp. 193-205
    • Stanić, Z.1
  • 40
    • 33947242274 scopus 로고    scopus 로고
    • Research problems from the Aveiro workshop on graph spectra
    • Stevanović D. Research problems from the Aveiro workshop on graph spectra. Linear Algebra Appl. 423 1 (2007) 172-181
    • (2007) Linear Algebra Appl. , vol.423 , Issue.1 , pp. 172-181
    • Stevanović, D.1
  • 41
    • 44649098816 scopus 로고    scopus 로고
    • Unoriented Laplacian maximizing graphs are degree maximal
    • Tam B.-S., Fan Y.-Z., and Zhou J. Unoriented Laplacian maximizing graphs are degree maximal. Linear Algebra Appl. 429 (2008) 735-758
    • (2008) Linear Algebra Appl. , vol.429 , pp. 735-758
    • Tam, B.-S.1    Fan, Y.-Z.2    Zhou, J.3
  • 42
    • 65049085914 scopus 로고    scopus 로고
    • On graphs whose signless Laplacian index does not exceed 4.5
    • Wang J., Huang Q., Belardo F., and Li Marzi E.M. On graphs whose signless Laplacian index does not exceed 4.5. Linear Algebra Appl. 431 (2009) 162-178
    • (2009) Linear Algebra Appl. , vol.431 , pp. 162-178
    • Wang, J.1    Huang, Q.2    Belardo, F.3    Li Marzi, E.M.4
  • 43
    • 33644863426 scopus 로고    scopus 로고
    • On the spectral characterization of T-shape trees
    • Wang W., and Xu C.-X. On the spectral characterization of T-shape trees. Linear Algebra Appl. 414 (2006) 492-501
    • (2006) Linear Algebra Appl. , vol.414 , pp. 492-501
    • Wang, W.1    Xu, C.-X.2
  • 44
    • 36949039458 scopus 로고    scopus 로고
    • On graphs whose spectral radius is bounded by frac(3, 2) sqrt(2)
    • Woo R., and Neumaier A. On graphs whose spectral radius is bounded by frac(3, 2) sqrt(2). Graphs Combin. 23 (2007) 713-726
    • (2007) Graphs Combin. , vol.23 , pp. 713-726
    • Woo, R.1    Neumaier, A.2
  • 45
    • 56549096913 scopus 로고    scopus 로고
    • On the maximal signless Laplacian spectral radius of graphs with given matching number
    • Yu G.-H. On the maximal signless Laplacian spectral radius of graphs with given matching number. Proc. Japan Acad. Ser. A 84 (2008) 163-166
    • (2008) Proc. Japan Acad. Ser. A , vol.84 , pp. 163-166
    • Yu, G.-H.1
  • 46
    • 67349174965 scopus 로고    scopus 로고
    • The lollipop graph is determined by its Q-spectrum
    • Zhang Y., Liu X., Zhang B., and Yong X. The lollipop graph is determined by its Q-spectrum. Discrete Math. 309 (2009) 3364-3369
    • (2009) Discrete Math. , vol.309 , pp. 3364-3369
    • Zhang, Y.1    Liu, X.2    Zhang, B.3    Yong, X.4
  • 47
    • 38349149310 scopus 로고    scopus 로고
    • A connection between ordinary and Laplacian spectra of bipartite graphs
    • Zhou B., and Gutman I. A connection between ordinary and Laplacian spectra of bipartite graphs. Linear and Multilinear Algebra 56 (2008) 305-310
    • (2008) Linear and Multilinear Algebra , vol.56 , pp. 305-310
    • Zhou, B.1    Gutman, I.2
  • 48
    • 44649130592 scopus 로고    scopus 로고
    • A study of graph spectra for comparing graphs and trees
    • Zhu P., and Wilson R.C. A study of graph spectra for comparing graphs and trees. Pattern Recogn. 41 9 (2008) 2833-2841
    • (2008) Pattern Recogn. , vol.41 , Issue.9 , pp. 2833-2841
    • Zhu, P.1    Wilson, R.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.