Author
Jason J. Molitierno
Other affiliations: University of Connecticut
Bio: Jason J. Molitierno is an academic researcher from Sacred Heart University. The author has contributed to research in topics: Algebraic connectivity & Laplacian matrix. The author has an hindex of 6, co-authored 13 publications receiving 153 citations. Previous affiliations of Jason J. Molitierno include University of Connecticut.
Papers
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TL;DR: In this paper, it was shown that the equality 1/Z(L#)=a(G) does not necessarily imply that 1/z(L #) satisfies the vertex connectivity constraint.
68 citations
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TL;DR: In this paper, the authors define the set Si,n to be the set of all integers from 0 to n, excluding i, and characterize the structures of the graphs whose Laplacian matrix has such a set as its eigenvalues.
Abstract: In this paper, we investigate graphs for which the corresponding Laplacian matrix has distinct integer eigenvalues. We define the set Si,n to be the set of all integers from 0 to n, excluding i. If there exists a graph whose Laplacian matrix has this set as its eigenvalues, we say that this set is Laplacian realizable. We investigate the sets Si,n that are Laplacian realizable, and the structures of the graphs whose Laplacian matrix has such a set as its eigenvalues. We characterize those i < n such that Si,n is Laplacian realizable, and show that for certain values of i, the set Si,n is realized by a unique graph. Finally, we conjecture that Sn,n is not Laplacian realizable for n ≥ 2 and show that the conjecture holds for certain values of n. © 2005 Wiley Periodicals, Inc. J Graph Theory
26 citations
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TL;DR: Quite tight lower and upper bounds are obtained on the algebraic connectivity, namely, the second-smallest eigenvalue of the Laplacian matrix, of an unweighted balanced binary tree with k levels and hence n = 2 1 vertices.
Abstract: In this paper, quite tight lower and upper bounds are obtained on the algebraic connectivity, namely, the second-smallest eigenvalue of the Laplacian matrix, of an unweighted balanced binary tree with k levels and hence n = 2 1 vertices This is accomplished by considering the inverse of a matrix of order k 1 readily obtained from the Laplacian matrix It is shown that the algebraic connectivity is 1=(2 2k + 3) +O(1=2)
23 citations
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TL;DR: In this paper, the algebraic connectivity of graphs of various genus has been studied and an upper bound on the connectivity of complete graphs of a fixed genus k is given, and the values of k for which the upper bound can be attained.
17 citations
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TL;DR: In this paper, the maximal diagonal entry of the group inverse of the Laplacian matrix of a tree and the pendant vertices of the tree with a perfect matching was studied.
12 citations
Cited by
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TL;DR: A survey of algebraic connectivity of a graph G is given in this paper, where the second smallest eigenvalue of the Laplacian of the graph G, denoted a(G), is considered.
385 citations
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TL;DR: In this paper, a lower bound on the second largest signless Laplacian eigenvalue and an upper bound for the smallest signless eigen value of a simple graph was given.
111 citations
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TL;DR: In this paper, the eigenvalues of the adjacency matrix and of the Laplacian matrix of an unweighted rooted tree of k levels such that in each level the vertices have equal degree were found.
72 citations
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TL;DR: In this paper, it was shown that the equality 1/Z(L#)=a(G) does not necessarily imply that 1/z(L #) satisfies the vertex connectivity constraint.
68 citations
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TL;DR: In this paper, the spectral scan statistic is proposed to find the sparsest cut in a graph, and its performance as a testing procedure depends directly on the spectrum of the graph and use this result to explicitly derive its asymptotic properties.
Abstract: We consider the change-point detection problem of deciding, based on noisy measurements, whether an unknown signal over a given graph is constant or is instead piecewise constant over two connected induced subgraphs of relatively low cut size. We analyze the corresponding generalized likelihood ratio (GLR) statistics and relate it to the problem of finding a sparsest cut in a graph. We develop a tractable relaxation of the GLR statistic based on the combinatorial Laplacian of the graph, which we call the spectral scan statistic, and analyze its properties. We show how its performance as a testing procedure depends directly on the spectrum of the graph, and use this result to explicitly derive its asymptotic properties on few significant graph topologies. Finally, we demonstrate both theoretically and by simulations that the spectral scan statistic can outperform naive testing procedures based on edge thresholding and $\chi^2$ testing.
66 citations