A graph, consisting of undirected edges, can be represented as a sum of two digraphs, consisting of oppositely oriented directed edges. Gutman and Plath in [J. Serb. Chem. Soc. 66 (2001), 237–241] showed that for annulenes, the eigenvalue spectrum of the graph is equal to the sum of the eigenvalue spectra of respective two digraphs. Here we exhibit a number of other graphs with this property.

Multi-protocol attacks due to protocol interaction has been a notorious problem for security. Gutman-Thayer proved that they can be prevented by ensuring that encrypted messages are distinguishable across protocols, under a free algebra [1]. In this paper, we prove that a similar suggestion prevents these attacks under commonly used operators such as Exclusive-OR, that induce equational theorie...

Florence F. Roussotte,1,3 Boris A. Gutman,3,4 Sarah K. Madsen,3,4 John B. Colby,1 and Paul M. Thompson1,2,3,4,5 for the Alzheimer’s Disease Neuroimaging Initiative* 1Department of Neurology, and 2Department of Psychiatry, Semel Institute, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California 90095, 3Imaging Genetics Center, and 4Departments of Neurology...

Recently, based on elementary geometry, Gutman proposed several geometry-based invariants (i.e., $SO$, $SO_{1}$, $SO_{2}$, $SO_{3}$, $SO_{4}$, $SO_{5}$, $SO_{6}$). The Sombor index was defined as $SO(G)=\sum\limits_{uv\in E(G)}\sqrt{d_{u}^{2}+d_{v}^{2}}$, the first $SO_{1}(G)= \frac{1}{2}\sum\limits_{uv\in E(G)}|d_{u}^{2}-d_{v}^{2}|$, where $d_{u}$ denotes degree of vertex $u$. In this paper, w...

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene polycyclic aromatic compounds. Recently, A family Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these may be successfully applied on modeling thermodynamic properties In this paper, we study expected values random hexagonal chains, consider some graphs such as g...

Please cite this article as: P.K. Douglas, Boris Gutman, Ariana Anderson, C. Larios, Katherine E. Lawrence, Katherine Narr, Biswa Sengupta, Gerald Cooray, David B. Douglas, Paul M. Thompson, James J. McGough, Susan Y. Bookheimer , Hemispheric brain asymmetry differences in youths with attention-deficit/hyperactivity disorder. The address for the corresponding author was captured as affiliation ...

Let [Formula: see text] be a simple graph with vertices, edges having Laplacian eigenvalues text]. The energy LE[Formula: is defined as text], where the average degree of Radenković and Gutman conjectured that among all trees order path has smallest energy. family diameter In this paper, we show any tree greater than thereby proving conjecture for We also truth number non-pendent vertices at mo...

We present estimates on the small singular values of a class of matrices with independent Gaussian entries and inhomogeneous variance profile, satisfying a broad-connectedness condition. Using these estimates and concentration of measure for the spectrum of Gaussian matrices with independent entries, we prove that for a large class of graphs satisfying an appropriate expansion property, the Bar...

Patentee(s): Yissum Research Development Company of The Hebrew University of Jerusalem of Hi Tech Park Edmond Safra Campus Givat-Ram PO Box 39135 Jerusalem 91390 Israel Inventor(s): Rav-Acha, Alexander Pritch, Yael Peleg, Shmuel Gutman, Avital Title: Method and system for video indexing and video synopsis Term: Twenty years from 9 December 2007 Date Accepted: 21 October 2011 Date Sealed: 23 Feb...