On The Decomposition Of The Line (Total) Graphs With Respct To Some Binary Operations
Graphs Which Are Switching Equivalent To Their Complementary Line Graphs II
Graphs Which Are Switching Equivalent To Their Complementary Line Graphs I
An Algorithm To Recognize A Generalized Line Graph And Output It's Root Graph
Some remarks on the complement of a line graph
On the Largest Eigenvalue of Unicyclic Graphs
Complementary Pairs of Graphs With the Second Largest Eigenvalue not Exceeding (sqrt(5)-1)/2
Graphs Which Are Switching Equivalent To Their Line Graphs
On the Largest Eigenvalue of some Homeomorphic Graphs
TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, I
Some additions to the theory of star partitions of graphs
This paper contains a number of results in the theory of star partitions of graphs. We illustrate a variety of situations which can arise when the Reconstruction Theorem for graphs is used, considering in particular galaxy graphs - these are graphs in which every star set is independent. We discuss a recursive ordering of graphs based on the Reconstruction Theorem, and point out the significance of galaxy graphs in this connection.
Relations between -regular sets and star complements
Let be a finite graph with an eigenvalue of multiplicity . A set of vertices in is called a star set for in if is not an eigenvalue of the star complement which is the subgraph of induced by vertices not in . A vertex subset of a graph is -regular if it induces a -regular subgraph and every vertex not in the subset has neighbors in it. We investigate the graphs having a -regular set which induces a star complement for some eigenvalue. A survey of known results is provided...
Graphs having planar complementary line (total) graphs.
A Note on Generalized Line Graphs
Graph equations for line graphs and n-th distance graphs.
A note on the graph equation .
On the largest eigenvalue of bicyclic graphs.
Tridiagonal matrices and spectral properties of some graph classes
A graph is called a chain graph if it is bipartite and the neighbourhoods of the vertices in each colour class form a chain with respect to inclusion. In this paper we give an explicit formula for the characteristic polynomial of any chain graph and we show that it can be expressed using the determinant of a particular tridiagonal matrix. Then this fact is applied to show that in a certain interval a chain graph does not have any nonzero eigenvalue. A similar result is provided for threshold graphs....
Some remarks on integral graphs with maximum degree four.
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