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1. A simple proof of Whitney's Theorem on connectivity in graphs

Creator:
Zhao, Kewen
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
connectivity and graph
Language:
English
Description:
In 1932 Whitney showed that a graph G with order n ≥ 3 is 2-connected if and only if any two vertices of G are connected by at least two internally-disjoint paths. The above result and its proof have been used in some Graph Theory books, such as in Bondy and Murty’s well-known Graph Theory with Applications. In this note we give a much simple proof of Whitney’s Theorem.
Rights:
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2. Connectivity of inferior carebellar peduncle in the human brain: A diffusion tensor imaging study

Creator:
Jang, S. H. and Kwon , H. G.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
inferior cerebellar peduncle, restiform body, connectivity, cerebellum, and diffusion tensor imaging
Language:
English
Description:
The inferior cerebellar peduncle (ICP) is an important role in motor control, such as coordination of movement control of balance, posture, and gait. In the current study, using diffusion tensor tractography (DTT), we attempted to investigate the connectivity of the ICP in normal subjects. Forty healthy subjects were recruited for this study. DTTs were acquired using a sensitivity-encoding head coil at 1.5 Tesla. A seed region of interest was drawn at the ICP using the FMRIB Software Library. Connectivity was defined as the incidence of connection between the ICP and target brain regions at the threshold of 5, 25, and 50 streamlines. The ICP showed 100% connectivity to the vestibular nucleus, reticular formation, pontine tegmentum, and posterior lobe of the cerebellum, irrespective of thresholds. In contrast, the ICP showed more than 70% connectivity with the target brain regions at the threshold of 5 streamlines that is to the thalamus (100 %), anterior lobe of the cerebellum (100 %), pedunculopontine nucleus (95.0 %), red nucleus (92.5 %), primary somatosensory cortex (86.3 %), and primary motor cortex (75.0 %). According to our findings, the ICP had high connectivity, mainly with the sensory-motor related areas. We believe that the methodology and results of this study would be useful in investigation of the neural network associated with the sensory-motor system and brain plasticity following brain injury and other diseases.
Rights:
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3. Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs

Creator:
Cioabă, Sebastian M and Gu, Xiaofeng
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, spectral graph theorye, igenvalue, connectivity, toughness, spanning k-tree, 13, and 51
Language:
English
Description:
The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity. We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree., Sebastian M. Cioabă, Xiaofeng Gu., and Obsahuje seznam literatury
Rights:
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4. On the connectivity of skeletons of pseudomanifolds with boundary

Creator:
Ayala, R., Chávez, M. J., Márquez, A., and Quintero, A.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
connectivity, graph, 2-complex, and pseudomanifolds
Language:
English
Description:
In this note we show that 1-skeletons and 2-skeletons of n-pseudomanifolds with full boundary are (n+ 1)-connected graphs and n-connected 2-complexes, respectively. This generalizes previous results due to Barnette and Woon.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. On the rupture degree of a graph

Creator:
Kirlangic, Alpay and Bacak-Turan , Goksen
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Networks, vulnerabity, connectivity, rupture degree, and complete k-ary tree
Language:
English
Description:
In a communication network, vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a connected graph as model-ing a network, the rupture degree of a graph is one measure of graph vulnerability and it is defined by r(G) = max{w(G-S)-|S|-m(G-S): S \subset V(G), w(G-S)>1} where w(G-S) is the number of components of G-S and m(G-S) is the order of a largest component of G-S. In this paper, general results on the rupture degree of a graph are considered. Firstly, some bounds on the rupture degree are given. Further, rupture degree of a complete k-ary tree is calculated. Also several results are given about complete k-ary tree and graph operations. Finally, we give formulas for the rupture degree of the cartesian product of some special graphs.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

6. Patch size and connectivity influence the population turnover of the threatened chequered blue butterfly, Scolitantides orion (Lepidoptera: Lycaenidae)

Creator:
Komonen, Atte, Tikkamäki, Tuuli, Mattila, Niina, and Kotiaho, Janne S.
Type:
article, model:article, and TEXT
Subject:
Butterfly conservation, colonization, connectivity, extinction, Lycaenidae, metapopulation, patch size, Scolitantides orion, Sedum telephium, and population turnover
Language:
English
Description:
Chequered blue butterfly, Scolitantides orion (Lepidoptera: Lycaenidae) has severely declined in many parts of Europe and is currently red-listed in many countries. We studied the population structure and turnover of the species in a lake-island system in a National Park in eastern Finland over a three-year period. The incidence of the chequered blue on the suitable islands (n = 41) and habitat patches (n = 123) was high: an average of 82% of the islands and patches were occupied over the three year period. At the island scale, the annual population turnover rate was 17%, with an extinction and colonization rate of 7% and 10%, respectively. At the patch scale, the annual population turnover was 16%, with 7% extinction and 9% colonization rate. Islands that were occupied over the three year period had a larger area of suitable habitat than islands in which turnover events were observed. At the patch scale, turnover events were observed in small and poorly connected patches. Patchy occurrence of the host plant and observed extinction-colonization dynamics suggest that the chequered blue population confirms a metapopulation structure. Although the local populations are small, the observed high patch occupancy and balanced population turnover indicates that the metapopulation is not in immediate risk of extinction.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

7. Photoadaptation in the green alga Spongiochloris sp. A three-fluorometer study

Creator:
Koblížek, M., Ciscato, M., Komenda, J., Kopecký, J., Šiffel, P., and Masojídek, J.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
chlorophyll fluorescence, photochemical yield, non-photochemical quenching, connectivity, and electron transport rate
Language:
Multiple languages
Description:
The dark-adapted cells of the green alga Spongiochloris sp. were exposed to "white light" of 1000 µmol(photon) m-2 s-1 for 2 h and then dark adapted for 1.5 h. Changes of photochemical activities during photoadaptation were followed by measurement of chlorophyll (Chl) fluorescence kinetics, 77 K emission spectra, photosynthetic oxygen evolution, and pigment composition. We observed a build-up of slowly-relaxing non-photochemical quenching which led to a decrease of the Fv/Fm parameter and the connectivity. In contrast to the depression of Fv/Fm (35 %) and the rise of non-photochemical quenching (∼ 1.6), we observed an increase in effective absorption cross-section (20 %), Hill reaction (30 %), photosynthetic oxygen evolution (80 %), and electron transport rate estimated from the Chl fluorescence analysis (80 %). We showed an inconsistency in the presently used interpretation schemes, and ascribe the discrepancy between the increase of effective absorption cross-section and the photosynthetic activities on one side and the effective non-photochemical quenching on the other side to the build-up of a quenching mechanism which dissipates energy in closed reaction centres. Such a type of quenching changes the ratio between thermal dissipation and fluorescence without any effect on photochemical yield. In this case the Fv/Fm ratio cannot be used as a measure of the maximum photochemical yield of PS2. and M. Koblížek ... [et al.].
Rights:
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8. Some algebraic properties of hypergraphs

Creator:
Emtander, Eric, Mohammadi, Fatemeh, and Moradi, Somayeh
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Betti numbers, chordal hypergraphs, connectivity, and homologically connected hypergraphs
Language:
English
Description:
We consider Stanley-Reisner rings $k[x_1,\ldots ,x_n]/I(\mathcal {H})$ where $I(\mathcal {H})$ is the edge ideal associated to some particular classes of hypergraphs. For instance, we consider hypergraphs that are natural generalizations of graphs that are lines and cycles, and for these we compute the Betti numbers. We also generalize some known results about chordal graphs and study a weak form of shellability.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

9. The edge-accessibility number via graph, operations & an algorithm

Creator:
Kilic, E. and Dundar, P.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Graph theory applications, connectivity, vulnerability and stability, computer communication networks and modeling, deterministic network models, accesibility, and edge-accessibility
Language:
English
Description:
In communications network design, network's stability is a very important concept. A network has to be constructed as possible as stable since the stability of a network shows its resistance to vulnerability. Many science and engineering problems can be represented by a network, generalization of which is a graph. Examples of problems that can be represented by a graph include: cyclic sequential circuit, organic molecule structures, mechanical structures, etc. So, a graph can be considered as a model of a communication network. Then, the notions of the graph theory can be used for the stability of a network. In the graph theory, deterministic measures of the stability are used for some parameters of graphs as connectivity, covering number, independence number and dominating number. Then, the stability of a network is defined with deterministic calculation. Today, these parameters take into consideration the neighborhood notion. Now, we consider an edge-accessibility number of a graph. Edge-accessibility is a notion which uses the neighborhood of edges (links). In this paper; we search the edge-accessibility number of a graph. We also give some theorems about the edge-accessibility using the graph operations and design an algorithm which found it with Time Complexity O(n3).
Rights:
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10. Two measures for the stability of Extended Fibonacci Cubes

Creator:
Dundar, P. and Kilic, E.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Network topology, neural network architecture, connectivity, quantitative modeling of networks, graph stability, and Extended Fibonacci Cubes
Language:
English
Description:
The Fibonacci Cube is an interconnection network that gets many desirable properties that are very important in the network design, network stability and applications. The extended Fibonacci Cube is a new network topology. The vulnerability value of a communication network shows the resistance of the network after the disruption of some centres or connection lines until the communication breakdown. In a network, as the number of centres belonging to sub networks changes, the vulnerability of the network also changes and requires greater degrees of stability or less vulnerability. If the communication network is modelled by graph G, the deterministic measures tend to provide a worst-case analysis of some aspects of overall disconnection process. Many graph theoretical parameters have been used in the past to describe the stability of communication networks. There are few parameters such as integrity, neighbour-integrity and tenacity number giving the vulnerability. Also, in the neighbour-integrity, if a station is destroyed, the adjacent stations will be betrayed so that the betrayed stations become useless to network as a whole. In this paper we study the stability of the Extended Fibonacci Cube using the integrity and neighbour-integrity. We compared the obtained results with the results of the other network topologies. We saw that, for two graphs G1 and G2 that have same number of vertices if k(G1) > k(G2), then I(G1) > I(G2) and NI(G1)< NI(G2).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public