循环图的距离能量（英文）
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摘要
For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph.
For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph.
For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph.
引文
[1]BUCKLEY F,HARARY F.Distance in Graphs[M].Redwood:Addison-Wesley,1990.
[2]INDULAL G,GUTMAN I.On the distance spectra of some graphs[J].Mathematical Communications,2008,13:123-131.
[3]JOVANOVIC I and STANIC Z.Spectral distances of graphs[J].Linear Algebra and its Applications,2012,436:1425-1435.
[4]INDULAL G.Sharp bounds on the distance spectral radius and the distance energy of graphs[J].Linear Algebra and its Applications,2009,430:106-113.
[5]GU J.The spectral distance based on the normalized Laplacian and applications to large networks[D].Leipzig:University of Leipzig,2014.
[6]INDULAL G,GUTMAN I,VIJAYKUMAR A.On distance energy of graphs[J].MATCH Communications in Mathematical and in Computer Chemistry,2008,60:461-472.
[7]RAMANE H S,REVANKAR D S,GUTMAN I,et al.Bounds for the distance energy of a graph[J].Kragujevac Journal of Mathematics,2008,31:59-68.
[8]HWANG F K.A survey on multi-loop networks[J].Theoretical Computer Science,2003,299:107-121.
[9]DAVIS P.Circulant Matrices[M].New York:John Wiley&Sons,1979.
[10]CVETKOVIC D M,DOOB M,SACHS H.Spectra of Graphs-Theory and Applications[M].New York:Academic Press,1980.
[11]ZHOU BO,ILIC ALEKSANDAR.On distance spectral radius and distance energy of graphs[J].MATCHCommunications in Mathematical and in Computer Chemistry,2010,64:261-280.
[12]NINA SABINE SCHMUCK.The Wiener index of a graph[D].Graz:Graz University of Technology,2010.
[13]MEIJE P T Connectivities and diameters of circulant graphs[D].Vancouver:Simon Fraser University,1991.
[2]INDULAL G,GUTMAN I.On the distance spectra of some graphs[J].Mathematical Communications,2008,13:123-131.
[3]JOVANOVIC I and STANIC Z.Spectral distances of graphs[J].Linear Algebra and its Applications,2012,436:1425-1435.
[4]INDULAL G.Sharp bounds on the distance spectral radius and the distance energy of graphs[J].Linear Algebra and its Applications,2009,430:106-113.
[5]GU J.The spectral distance based on the normalized Laplacian and applications to large networks[D].Leipzig:University of Leipzig,2014.
[6]INDULAL G,GUTMAN I,VIJAYKUMAR A.On distance energy of graphs[J].MATCH Communications in Mathematical and in Computer Chemistry,2008,60:461-472.
[7]RAMANE H S,REVANKAR D S,GUTMAN I,et al.Bounds for the distance energy of a graph[J].Kragujevac Journal of Mathematics,2008,31:59-68.
[8]HWANG F K.A survey on multi-loop networks[J].Theoretical Computer Science,2003,299:107-121.
[9]DAVIS P.Circulant Matrices[M].New York:John Wiley&Sons,1979.
[10]CVETKOVIC D M,DOOB M,SACHS H.Spectra of Graphs-Theory and Applications[M].New York:Academic Press,1980.
[11]ZHOU BO,ILIC ALEKSANDAR.On distance spectral radius and distance energy of graphs[J].MATCHCommunications in Mathematical and in Computer Chemistry,2010,64:261-280.
[12]NINA SABINE SCHMUCK.The Wiener index of a graph[D].Graz:Graz University of Technology,2010.
[13]MEIJE P T Connectivities and diameters of circulant graphs[D].Vancouver:Simon Fraser University,1991.