Distance spectral radius of trees with fixed maximum degree.
The minimum spectral radius of graphs with a given clique number.
All graphs in which each pair of distinct vertices has exactly two common neighbors
We find all connected graphs in which any two distinct vertices have exactly two common neighbors, thus solving a problem by B. Zelinka.
ON RELATION BETWEEN SPECTRA OF GRAPHS AND THEIR DIGRAPH DECOMPOSITIONS
Graphs with Least Eigenvalue at Least -sqrt(3)
Some Trees Characterized by Eigenvalues and Angles
Applications of Graph Spectra in Quantum Physics
Variable neighborhood search for extremal graphs. 17. Further conjectures and results about the index
The AutoGraphiX 2 system is used to compare the index of a connected graph G with a number of other graph theoretical invariants, i.e., chromatic number, maximum, minimum and average degree, diameter, radius, average distance, independence and domination numbers. In each case, best possible lower and upper bounds, in terms of the order of G, are sought for sums, differences, ratios and products of the index and another invariant. There are 72 cases altogether: in 7 cases known results were reproduced,...
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