scholarly journals Seidel energy of iterated line graphs of regular graphs

2015 ◽  
Vol 39 (1) ◽  
pp. 7-12 ◽  
Author(s):  
Harishchandra Ramane ◽  
Ivan Gutman ◽  
Mahadevappa Gundloor
Keyword(s):  
Line Graphs ◽  
Regular Graphs

scholarly journals Spectra and energies of iterated line graphs of regular graphs

2005 ◽  
Vol 18 (6) ◽  
pp. 679-682 ◽  
Author(s):  
H.S. Ramane ◽  
H.B. Walikar ◽  
S.B. Rao ◽  
B.D. Acharya ◽  
P.R. Hampiholi ◽  
...  
Keyword(s):  
Line Graphs ◽  
Regular Graphs

scholarly journals Towards a spectral theory of graphs based on the signless Laplacian, I

2009 ◽  
Vol 85 (99) ◽  
pp. 19-33 ◽  
Author(s):  
Dragos Cvetkovic ◽  
Slobodan Simic
Keyword(s):  
Graph Theory ◽  
Spectral Theory ◽  
Spectral Graph Theory ◽  
Line Graphs ◽  
Regular Graphs ◽  
Spectral Graph ◽  
Q Theory ◽  
Signless Laplacian ◽  
M Theory ◽  
Theory Of Graphs

A spectral graph theory is a theory in which graphs are studied by means of eigenvalues of a matrix M which is in a prescribed way defined for any graph. This theory is called M-theory. We outline a spectral theory of graphs based on the signless Laplacians Q and compare it with other spectral theories, in particular with those based on the adjacency matrix A and the Laplacian L. The Q-theory can be composed using various connections to other theories: equivalency with A-theory and L-theory for regular graphs, or with L-theory for bipartite graphs, general analogies with A-theory and analogies with A-theory via line graphs and subdivision graphs. We present results on graph operations, inequalities for eigenvalues and reconstruction problems.

scholarly journals Some Properties of Regular Line Graphs

2008 ◽  
pp. 44-49
Keyword(s):  
Key Words ◽  
Bipartite Graph ◽  
Line Graph ◽  
Bipartite Graphs ◽  
Line Graphs ◽  
Sufficient Condition ◽  
Regular Graphs ◽  
Necessary And Sufficient Condition ◽  
Regular Line ◽  
Necessary And Sufficient

In this paper, the concept of regular line graph has been introduced. The maximum number of vertices with different degrees in the regular line graphs has also been studied. Further, the necessary and sufficient condition for regular line graph to be bipartite graph have also been proved. Key words: Line Graphs, Regular graphs, Connected graphs, Bipartite Graphs.

scholarly journals The asymptotic behavior of some indices of iterated line graphs of regular graphs

2012 ◽  
Vol 160 (7-8) ◽  
pp. 1232-1239 ◽  
Author(s):  
Weigen Yan ◽  
Yeong-Nan Yeh ◽  
Fuji Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Line Graphs ◽  
Regular Graphs
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