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ON THE NULL-SPACES OF BICYCLIC SINGULAR GRAPHS
Discrete Mathematics, Algorithms and Applications, 2011In [M. Nath and B. K. Sarma, On the null-spaces of unicyclic and acyclic graphs, Linear Algebra Appl.427 (2007) 42–54], Nath and Sarma gave an algorithm to find a basis for the null-space of a graph G when G is singular acyclic or unicyclic. In this paper, we find a basis for the null-space of G when G is a bicyclic singular graph.
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Exploring the Embedding of the Extended Zero-Divisor Graph of Commutative Rings
AxiomsRc represents commutative rings that have unity elements. The collection of all zero-divisor elements in Rc are represented by D(Rc). We denote an extended zero-divisor graph by the notation ℸ′(Rc) of Rc. This graph has a set of vertices in D(Rc)*.
A. Khabyah, M. A. Ansari
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2016
In the last chapter, a qualitative comparison of various real-world structures with classic random graph models revealed that complex networks are non-random in many aspects. This chapter focuses on the question of how to quantify the statistical significance of an observed network structure with respect to a given random graph model.
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In the last chapter, a qualitative comparison of various real-world structures with classic random graph models revealed that complex networks are non-random in many aspects. This chapter focuses on the question of how to quantify the statistical significance of an observed network structure with respect to a given random graph model.
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Explainable Global Wildfire Prediction Models using Graph Neural Networks
arXiv.orgWildfire prediction has become increasingly crucial due to the escalating impacts of climate change. Traditional CNN-based wildfire prediction models struggle with handling missing oceanic data and addressing the long-range dependencies across distant ...
Dayou Chen +4 more
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Half-integral Erdös-Pósa property for non-null S-T paths
arXiv.orgFor a group $\Gamma$, a $\Gamma$-labelled graph is an undirected graph $G$ where every orientation of an edge is assigned an element of $\Gamma$ so that opposite orientations of the same edge are assigned inverse elements.
Vera Chekan +6 more
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IEEE Transactions on Signal Processing
The detection of interesting or anomalous signal behavior using sensor networks plays a key role in many applications. In this work, we model the sensor network as a graph, with each vertex representing a sensor and a signal over time associated with ...
Xingchao Jian +4 more
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The detection of interesting or anomalous signal behavior using sensor networks plays a key role in many applications. In this work, we model the sensor network as a graph, with each vertex representing a sensor and a signal over time associated with ...
Xingchao Jian +4 more
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AMS/MAA Textbooks, 2018
A graph is a system G = (V, E) consisting of a set V of vertices and a set E (disjoint from V ) of edges, together with an incidence function End : E → M2(V ), where M2(V ) is set of all 2-element sub-multisets of V . We usually write V = V (G), E = E(G),
L. Gladkov
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A graph is a system G = (V, E) consisting of a set V of vertices and a set E (disjoint from V ) of edges, together with an incidence function End : E → M2(V ), where M2(V ) is set of all 2-element sub-multisets of V . We usually write V = V (G), E = E(G),
L. Gladkov
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Counting Graphs and Null Models of Complex Networks: Configuration Model and Extensions
2017Due to its ease of use, as well as its enormous flexibility in its degree structure, the configuration model has become the network model of choice in many disciplines. It has the wonderful property, that, conditioned on being simple, it is a uniform random graph with the prescribed degrees. This is a beautiful example of a general technique called the
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Null bar and null zone are better than the error bar to compare group means in graphs
Journal of Clinical Epidemiology, 2004Conventional graphs often include error bars around the group means. Regardless of what these bars depict, they are uninformative as to whether a difference between the groups is statistically significant.This article suggests plotting the null bar or null zone: that is, the range or area in which the means of the two groups fall if the null hypothesis
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Irreducible components of canonical graphs for second order spectral nulls
Proceedings of IEEE International Symposium on Information Theory, 2002Irreducible components of canonical graphs for second order spectral null constraints at a frequency f=f/sub s/k/n, where f/sub s/ is the symbol frequency, and k and n, integers with k/spl ges/0 and n>0. We show that if n is prime then a canonical graph consists of disjoint irreducible components.
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