The distance spectrum of a tree
Journal of Graph Theory
Average distance and independence number
2nd Twente workshop on Graphs and combinatorial optimization
On acyclic conjugated molecules with minimal energies
Discrete Applied Mathematics
Introduction to Algorithms
On acyclic systems with minimal Hosoya index
Discrete Applied Mathematics
On the minimal energy ordering of trees with perfect matchings
Discrete Applied Mathematics
Note: On extremal unicyclic molecular graphs with maximal Hosoya index
Discrete Applied Mathematics
Distance spectral spread of a graph
Discrete Applied Mathematics
The distance spectral radius of digraphs
Discrete Applied Mathematics
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The distance spectral radius @r(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Recently, many researches proposed the use of @r(G) as a molecular structure descriptor of alkanes. In this paper, we introduce general transformations that decrease distance spectral radius and characterize n-vertex trees with given matching number m which minimize the distance spectral radius. The extremal tree A(n,m) is a spur, obtained from the star graph S"n"-"m"+"1 with n-m+1 vertices by attaching a pendent edge to each of certain m-1 non-central vertices of S"n"-"m"+"1. The resulting trees also minimize the spectral radius of adjacency matrix, Hosoya index, Wiener index and graph energy in the same class of trees. In conclusion, we pose a conjecture for the maximal case based on the computer search among trees on n@?24 vertices. In addition, we found the extremal tree that uniquely maximizes the distance spectral radius among n-vertex trees with perfect matching and fixed maximum degree @D.