Browsing by Author "Leydold, Josef"
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Algebraic connectivity and degree sequences of trees
Bıyıkoğlu, Türker; Leydold, Josef (ELSEVIER SCIENCE INC, 20090115)We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are nondecreasing on every ... 
Dendrimers are the unique chemical trees with maximum spectral radius
Bıyıkoğlu, Türker; Leydold, Josef (UNIV KRAGUJEVAC, 2012)It is shown that dendrimers have maximum spectral radius and maximum CollatzSinogowitz index among all chemical trees of given size. The result is also generalized for the class of chemical trees with prescribed number ... 
Graphs of given order and size and minimum algebraic connectivity
Bıyıkoğlu, Türker; Leydold, Josef (ELSEVIER SCIENCE INC, 20120401)The structure of connected graphs of given size and order that have minimal algebraic connectivity is investigated. It is shown that they must consist of a chain of cliques. Moreover, an upper bound for the number of maximal ... 
Graphs with given degree sequence and maximal spectral radius
Bıyıkoğlu, Türker; Leydold, Josef (ELECTRONIC JOURNAL OF COMBINATORICS, 20080915)We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is nonincreasing with respect ... 
Largest Eigenvalues of The Discrete PLaplacian of Trees with Degree
Bıyıkoğlu, Türker; Hellmuth, Marc; Leydold, Josef (INT LINEAR ALGEBRA SOC, C/O JAMES WEAVER DEPT MATH & STATISTICS, 200903)Trees that have greatest maximum pLaplacian eigenvalue among all trees with a given degree sequence are characterized. It is shown that such extremal trees can be obtained by breadthfirst search where the vertex degrees ... 
LARGEST EIGENVALUES OF THE DISCRETE PLAPLACIAN OF TREES WITH DEGREE SEQUENCES
Biyikoglu, Tuerker; Hellmuth, Marc; Leydold, Josef (INT LINEAR ALGEBRA SOC, 2009)Trees that have greatest maximum pLaplacian eigenvalue among all trees with a given degree sequence are characterized. It is shown that such extremal trees can be obtained by breadthfirst search where the vertex degrees ... 
Semiregular trees with minimal Laplacian spectral radius
Bıyıkoğlu, Türker; Leydold, Josef (Elsevier Inc, 20100415)A semiregular tree is a tree where all nonpendant vertices have the same degree. Among all semiregular trees with fixed order and degree, a graph with minimal (adjacency/Laplacian) spectral radius is a caterpillar. Counter ...