Results 141 to 150 of about 1,706,764 (337)

Integral trees of odd diameters [PDF]

open access: yesarXiv, 2010
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvari proved the existence of integral trees of any even diameter. In the odd case, integral trees have been constructed with diameter at most 7.
arxiv  

On super edge-graceful trees of diameter four [PDF]

open access: yesarXiv, 2011
In "On the super edge graceful trees of even orders," Chung, Lee, Gao, and Schaffer posed the following problem: Characterize trees of diameter 4 which are super edge-graceful. In this paper, we provide super edge-graceful labelings for all caterpillars and even size lobsters of diameter 4 which permit such labelings.
arxiv  

The anterior nucleus of the thalamus plays a role in the epileptic network

open access: yesAnnals of Clinical and Translational Neurology, Volume 9, Issue 12, Page 2010-2024, December 2022., 2022
Abstract Objectives We investigated both the metabolic differences and interictal/ictal discharges of the anterior nucleus of the thalamus (ANT) in patients with epilepsy to clarify the relationship between the ANT and the epileptic network. Methods Nineteen patients with drug‐resistant epilepsy who underwent stereoelectroencephalography were studied ...
Hao Yan   +9 more
wiley   +1 more source

Rainbow connection of bridgeless outerplanar graphs with small diameters [PDF]

open access: yesarXiv, 2016
In this paper, we investigate rainbow connection number $rc(G)$ of bridgeless outerplanar graphs $G$ with diameter 2 or 3. We proved the following results: If $G$ has diameter $2,$ then $rc(G)=3$ for fan graphs $F_{n}$ with $n\geq 7$ or $C_5,$ otherwise $rc(G)=2;$ if $G$ has diameter $3,$ then $rc(G)\leq 4$ and the bound is sharp.
arxiv  

Structure fault diameter of hypercubes [PDF]

open access: yesarXiv
Structure connectivity and substructure connectivity are innovative indicators for assessing network reliability and fault tolerance. Similarly, fault diameter evaluates fault tolerance and transmission delays in networks. This paper extends the concept of fault diameter by introducing two new variants: structure fault diameter and substructure fault ...
arxiv  

Quantum algorithms and lower bounds for eccentricity, radius, and diameter in undirected graphs [PDF]

open access: yesarXiv
The problems of computing eccentricity, radius, and diameter are fundamental to graph theory. These parameters are intrinsically defined based on the distance metric of the graph. In this work, we propose quantum algorithms for the diameter and radius of undirected, weighted graphs in the adjacency list model.
arxiv  

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