scholarly journals Edge-Labeling Based Directed Gated Graph Network for Few-Shot Learning

2021 ◽  
Author(s):  
Peixiao Zheng ◽  
Xin Guo ◽  
Lin Qi
Keyword(s):  
Edge Labeling

scholarly journals On the Topology of the Cambrian Semilattices

10.37236/2910 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Myrto Kallipoliti ◽  
Henri Mühle
Keyword(s):  
Coxeter Group ◽  
Closed Interval ◽  
Open Interval ◽  
Weak Order ◽  
Edge Labeling

For an arbitrary Coxeter group $W$, Reading and Speyer defined Cambrian semilattices $\mathcal{C}_{\gamma}$ as sub-semilattices of the weak order on $W$ induced by so-called $\gamma$-sortable elements. In this article, we define an edge-labeling of $\mathcal{C}_{\gamma}$, and show that this is an EL-labeling for every closed interval of $\mathcal{C}_{\gamma}$. In addition, we use our labeling to show that every finite open interval in a Cambrian semilattice is either contractible or spherical, and we characterize the spherical intervals, generalizing a result by Reading.

scholarly journals Cryptosystem using double vertex graph

2020 ◽  
Vol 13 (44) ◽  
pp. 4483-4489
Author(s):  
C Beaula ◽  
Keyword(s):  
Graph Theory ◽  
Secure Communication ◽  
System Method ◽  
Encryption And Decryption ◽  
Vertex Graph ◽  
Private And Public ◽  
Almost All ◽  
Encryption Method ◽  
The Given ◽  
Edge Labeling

Background/Objective: The Coronavirus Covid-19 has affected almost all the countries and millions of people got infected and more deaths have been reported everywhere. The uncertainty and fear created by the pandemic can be used by hackers to steal the data from both private and public systems. Hence, there is an urgent need to improve the security of the systems. This can be done only by building a strong cryptosystem. So many researchers started embedding different topics of mathematics like algebra, number theory, and so on in cryptography to keep the system, safe and secure. In this study, a cryptosystem using graph theory has been attempted, to strengthen the security of the system. Method: A new graph is constructed from the given graph, known as a double vertex graph. The edge labeling of this double vertex graph is used in encryption and decryption. Findings: A new cryptosystem using the amalgamation of the path, its double vertex graph and edge labeling has been proposed. From the double vertex graph of a path, we have given a method to find the original path. To hack such an encrypted key, the knowledge of graph theory is important, which makes the system stronger. Applications:The one-word encryption method will be useful in every security system that needs a password for secure communication or storage or authentication. Keywords: Double vertex graphs; path; adjacency matrix; encryption; cryptography

scholarly journals Computational complexity of distance edge labeling

2018 ◽  
Vol 246 ◽  
pp. 80-98
Author(s):  
Dušan Knop ◽  
Tomáš Masařík
Keyword(s):  
Computational Complexity ◽  
Edge Labeling

scholarly journals Vertex Equitable Labeling of Cycle and Star Related Graphs

2015 ◽  
Vol 7 (3) ◽  
pp. 33-42
Author(s):  
P. Jeyanthi ◽  
A. Maheswari ◽  
M, Vijaya-Laksmi
Keyword(s):  
Mean Value ◽  
Edge Labeling

Let G be a graph with p vertices and q edges and A = {0,1,2,…..,[q/2]} A vertex labeling f: V (G) ? A induces an edge labeling f* defined by f*(uv) = f(u) + f(v) for all edges uv. For ? ? A, let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |?f (?) - ?f (b)|? 1 and the induced edge labels are 1, 2, 3,…, q. In this paper, we prove that jewel graph Jn, jelly fish graph (JF)n, balanced lobster graph BL(n,2,m), Ln ? Km (mean value) and <LnôK1,m> are vertex equitable graphs.  

OPTIMAL CONSTRUCTION OF SENSE OF DIRECTION IN A TORUS BY A MOBILE AGENT

2007 ◽  
Vol 18 (03) ◽  
pp. 529-546 ◽  
Author(s):  
HANANE BECHA ◽  
PAOLA FLOCCHINI
Keyword(s):  
Mobile Agent ◽  
Message Passing ◽  
Sense Of Direction ◽  
Optimal Construction ◽  
Edge Labeling

Sense of direction is a property of the edge-labeling of a network whose availability facilitates computations and often decreases their complexity. In this paper we consider the problem of providing a sense of direction to an anonymous, unoriented torus. The edges of the torus are initially labeled arbitrarily, and they have to be relabeled with a classical compass sense of direction. We first describe an algorithm where the relabeling of the edges is performed by a mobile agent that carries a token. The algorithm is optimal both in terms of number of tokens (with no tokens the task cannot be performed), and in terms of number of moves. We then show that the same technique can be used to orient the torus in the classical message-passing environment, thus obtaining an orientation algorithm that improves all the existing ones in this setting.

Lucky Edge Labeling of Triangular Graphs

2016 ◽  
Vol 36 (2) ◽  
pp. 116-118
Author(s):  
A.Nellai Murugan ◽  
◽  
R.Maria Irudhaya Aspin Chitra
Keyword(s):  
Edge Labeling

On effective and efficient graph edge labeling

2018 ◽  
Vol 37 (1) ◽  
pp. 5-38 ◽  
Author(s):  
Oshini Goonetilleke ◽  
Danai Koutra ◽  
Kewen Liao ◽  
Timos Sellis
Keyword(s):  
Edge Labeling

On Edge-Balance Index Sets of the Graph CnxP6(n=3,4,5mod6)

2011 ◽  
Vol 339 ◽  
pp. 662-665
Author(s):  
Yu Rong Ji ◽  
Ai Jun Li ◽  
Jing Jing Yao
Keyword(s):  
Simple Graph ◽  
Index Sets ◽  
Vertex Set ◽  
Binary Edge ◽  
Balance Index ◽  
Edge Labeling

Let G be a simple graph with vertex set V(G) and edge set E(G), and let Z2 = {0,1}. For a given binary edge labeling f :E(G)→Z2 , the edge labeling f induces a partial vertex labeling f*:V(G)→Z2 such that f*(v) =1(0) iff the number of 1-edges (0-edges) is strictly greater than the number of 0-edges (1-edges) incident to v , otherwise f*(v) is idefined. For i∈Z2 , let v(i)=card{v∈V(G): f*(v) =i} and e(i) = card{e∈E(G) : f (e)=i}. The edge-balance index sets of a graph G,EBI(G), is defined as {|v(0) −v(1) |: the edge labeling f satisfies |e(0)−e(1) |≤1}.In this paper, we completely determine the edge-balance CnxP 6(n=3,4,5mod6).

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