scholarly journals Results on Independent Sets in Categorical Products of Graphs, the Ultimate Categorical Independence Ratio and the Ultimate Categorical Independent Domination Ratio

2014 ◽  
pp. 237-248
Author(s):  
Wing-Kai Hon ◽  
Ton Kloks ◽  
Ching-Hao Liu ◽  
Hsiang-Hsuan Liu ◽  
Sheung-Hung Poon ◽  
...  
Keyword(s):  
Independent Sets ◽  
Independent Domination

scholarly journals An Improved Nordhaus–Gaddum-Type Theorem for 2-Rainbow Independent Domination Number

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 402
Author(s):  
Enqiang Zhu
Keyword(s):  
Applied Mathematics ◽  
Domination Number ◽  
Type Theorem ◽  
Independent Sets ◽  
Independent Domination ◽  
Integer Labeling ◽  
Vertex Disjoint

For a graph G, its k-rainbow independent domination number, written as γrik(G), is defined as the cardinality of a minimum set consisting of k vertex-disjoint independent sets V1,V2,…,Vk such that every vertex in V0=V(G)\(∪i=1kVi) has a neighbor in Vi for all i∈{1,2,…,k}. This domination invariant was proposed by Kraner Šumenjak, Rall and Tepeh (in Applied Mathematics and Computation 333(15), 2018: 353–361), which aims to compute the independent domination number of G□Kk (the generalized prism) via studying the problem of integer labeling on G. They proved a Nordhaus–Gaddum-type theorem: 5≤γri2(G)+γri2(G¯)≤n+3 for any n-order graph G with n≥3, in which G¯ denotes the complement of G. This work improves their result and shows that if G≇C5, then 5≤γri2(G)+γri2(G¯)≤n+2.

Trees without twin-leaves with smallest number of maximal independent sets

2020 ◽  
Vol 30 (1) ◽  
pp. 53-67 ◽  
Author(s):  
Dmitriy S. Taletskii ◽  
Dmitriy S. Malyshev
Keyword(s):  
Independent Sets ◽  
Adjacent Vertex ◽  
Maximal Independent Sets

AbstractFor any n, in the set of n-vertex trees such that any two leaves have no common adjacent vertex, we describe the trees with the smallest number of maximal independent sets.

scholarly journals Covering Small Independent Sets and Separators with Applications to Parameterized Algorithms

2020 ◽  
Vol 16 (3) ◽  
pp. 1-31
Author(s):  
Daniel Lokshtanov ◽  
Fahad Panolan ◽  
Saket Saurabh ◽  
Roohani Sharma ◽  
Meirav Zehavi
Keyword(s):  
Independent Sets ◽  
Parameterized Algorithms

Independent sets in n-vertex k-chromatic ℓ-connected graphs

2021 ◽  
Vol 344 (7) ◽  
pp. 112376
Author(s):  
John Engbers ◽  
Lauren Keough ◽  
Taylor Short
Keyword(s):  
Independent Sets ◽  
Connected Graphs

scholarly journals Independent domination in subcubic graphs

2021 ◽  
Author(s):  
A. Akbari ◽  
S. Akbari ◽  
A. Doosthosseini ◽  
Z. Hadizadeh ◽  
Michael A. Henning ◽  
...  
Keyword(s):  
Independent Domination ◽  
Subcubic Graphs

scholarly journals Coincidence counter measurements of cosmic rays in an aeroplane

1936 ◽  
Vol 156 (889) ◽  
pp. 570-577 ◽  
Keyword(s):  
Cosmic Rays ◽  
High Altitude ◽  
Cosmic Ray ◽  
Independent Sets ◽  
Vertical Line ◽  
Coincidence Counting ◽  
Detailed Design ◽  
Recording Apparatus ◽  
Coincidence Counter ◽  
Balloon Experiments

Cosmic ray measurements on mountains are limited in general to altitudes below about 4000 meters. Above this height Regener has made successful use of small balloons carrying self-recording apparatus, and occasional flights have been made with manned balloons by Piccard, Cosyns, and by American workers. Balloon experiments are, however, hardly practicable in this country, so we decided to investigate cosmic rays, and in particular the production of showers, using an aeroplane. Facilities for flying to a height of about 10 km. Were generously provided by the Air Ministry. Apparatus Two independent sets of three tube counters were used in conjunction with the usual coincidence counting circuits. The counters could be arranged in a vertical line to record vertical penetrating particles, or in a triangle to record showers. The triple coincidences were recorded by telephone counters which were photographed at intervals together with a clock and aneroid barometer. The detailed design of the apparatus required some consideration since the aeroplane available (the Vickers Vespa machine used for high altitude experiments at the Royal Aircraft Establishment) had an open observer’s cockpit in which the counting set had to be installed.

On graphs with the third largest number of maximal independent sets

2009 ◽  
Vol 109 (4) ◽  
pp. 248-253 ◽  
Author(s):  
Hongbo Hua ◽  
Yaoping Hou
Keyword(s):  
Independent Sets ◽  
The Third ◽  
Maximal Independent Sets
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