scholarly journals Local edge coloring of graphs

2021 ◽  
pp. 1-8
Author(s):  
P. Deepa ◽  
P. Srinivasan ◽  
M. Sundarakannan
Keyword(s):  
Edge Coloring ◽  
Local Edge

scholarly journals Super local edge anti-magic total coloring of paths and its derivation

2020 ◽  
Vol 3 (2) ◽  
pp. 126
Author(s):  
Fawwaz Fakhrurrozi Hadiputra ◽  
Denny Riama Silaban ◽  
Tita Khalis Maryati
Keyword(s):  
Chromatic Number ◽  
Minimum Weight ◽  
Edge Coloring ◽  
Simple Graph ◽  
Total Coloring ◽  
Local Edge

<p>Suppose <em>G</em>(<em>V,E</em>) be a connected simple graph and suppose <em>u,v,x</em> be vertices of graph <em>G</em>. A bijection <em>f</em> : <em>V</em> ∪ <em>E</em> → {1,2,3,...,|<em>V</em> (<em>G</em>)| + |<em>E</em>(<em>G</em>)|} is called super local edge antimagic total labeling if for any adjacent edges <em>uv</em> and <em>vx</em>, <em>w</em>(<em>uv</em>) 6= <em>w</em>(<em>vx</em>), which <em>w</em>(<em>uv</em>) = <em>f</em>(<em>u</em>)+<em>f</em>(<em>uv</em>)+<em>f</em>(<em>v</em>) for every vertex <em>u,v,x</em> in <em>G</em>, and <em>f</em>(<em>u</em>) &lt; <em>f</em>(<em>e</em>) for every vertex <em>u</em> and edge <em>e</em> ∈ <em>E</em>(<em>G</em>). Let γ(<em>G</em>) is the chromatic number of edge coloring of a graph <em>G</em>. By giving <em>G</em> a labeling of <em>f</em>, we denotes the minimum weight of edges needed in <em>G</em> as γ<em>leat</em>(<em>G</em>). If every labels for vertices is smaller than its edges, then it is be considered γ<em>sleat</em>(<em>G</em>). In this study, we proved the γ sleat of paths and its derivation.</p>

scholarly journals On The Local Edge Antimagic Coloring of Corona Product of Path and Cycle

CAUCHY ◽  
2019 ◽  
Vol 6 (1) ◽  
pp. 40
Author(s):  
Siti Aisyah ◽  
Ridho Alfarisi ◽  
Rafiantika M. Prihandini ◽  
Arika Indah Kristiana ◽  
Ratna Dwi Christyanti
Keyword(s):  
Chromatic Number ◽  
Connected Graph ◽  
Edge Coloring ◽  
Antimagic Labeling ◽  
Proper Edge Coloring ◽  
Minimum Number ◽  
Vertex Set ◽  
Local Edge ◽  
Corona Product

<p>Let  be a nontrivial and connected graph of vertex set  and edge set  . A bijection  is called a local edge antimagic labeling if for any two adjacent edges  and , where for . Thus, the local edge antimagic labeling induces a proper edge coloring of G if each edge e assigned the color  . The color of each an edge <em>e</em> = <em>uv</em> is assigned bywhich is defined by the sum of label both and vertices  and  . The local edge antimagic chromatic number, denoted by  is the minimum number of colors taken over all colorings induced by local edge antimagic labeling of   . In our paper, we present the local edge antimagic coloring of corona product of path and cycle, namely path corona cycle, cycle corona path, path corona path, cycle corona cycle.</p><p><strong>Keywords:</strong> Local antimagic; edge coloring; corona product; path; cycle.</p>

A STUDY ON FUZZY EQUITABLE EDGE COLORING OF WHEEL RELATED GRAPHS

2020 ◽  
Vol 9 (11) ◽  
pp. 9311-9317
Author(s):  
K. Sivaraman ◽  
R.V. Prasad
Keyword(s):  
Edge Coloring ◽  
Graph Labeling ◽  
Equitable Edge Coloring

Equitable edge coloring is a kind of graph labeling with the following restrictions. No two adjacent edges receive same label (color). and number of edges in any two color classes differ by at most one. In this work we are going to present the Fuzzy equitable edge coloring of some wheel related graphs.

Machine Learning Based Assembly of Fragments of Ancient Papyrus

2021 ◽  
Vol 14 (3) ◽  
pp. 1-21
Author(s):  
Roy Abitbol ◽  
Ilan Shimshoni ◽  
Jonathan Ben-Dov
Keyword(s):  
Machine Learning ◽  
Spatial Information ◽  
Real Life ◽  
Dead Sea ◽  
Machine Learning Techniques ◽  
Automated Classification ◽  
Learning Techniques ◽  
Test Batch ◽  
Validation Set ◽  
Local Edge

The task of assembling fragments in a puzzle-like manner into a composite picture plays a significant role in the field of archaeology as it supports researchers in their attempt to reconstruct historic artifacts. In this article, we propose a method for matching and assembling pairs of ancient papyrus fragments containing mostly unknown scriptures. Papyrus paper is manufactured from papyrus plants and therefore portrays typical thread patterns resulting from the plant’s stems. The proposed algorithm is founded on the hypothesis that these thread patterns contain unique local attributes such that nearby fragments show similar patterns reflecting the continuations of the threads. We posit that these patterns can be exploited using image processing and machine learning techniques to identify matching fragments. The algorithm and system which we present support the quick and automated classification of matching pairs of papyrus fragments as well as the geometric alignment of the pairs against each other. The algorithm consists of a series of steps and is based on deep-learning and machine learning methods. The first step is to deconstruct the problem of matching fragments into a smaller problem of finding thread continuation matches in local edge areas (squares) between pairs of fragments. This phase is solved using a convolutional neural network ingesting raw images of the edge areas and producing local matching scores. The result of this stage yields very high recall but low precision. Thus, we utilize these scores in order to conclude about the matching of entire fragments pairs by establishing an elaborate voting mechanism. We enhance this voting with geometric alignment techniques from which we extract additional spatial information. Eventually, we feed all the data collected from these steps into a Random Forest classifier in order to produce a higher order classifier capable of predicting whether a pair of fragments is a match. Our algorithm was trained on a batch of fragments which was excavated from the Dead Sea caves and is dated circa the 1st century BCE. The algorithm shows excellent results on a validation set which is of a similar origin and conditions. We then tried to run the algorithm against a real-life set of fragments for which we have no prior knowledge or labeling of matches. This test batch is considered extremely challenging due to its poor condition and the small size of its fragments. Evidently, numerous researchers have tried seeking matches within this batch with very little success. Our algorithm performance on this batch was sub-optimal, returning a relatively large ratio of false positives. However, the algorithm was quite useful by eliminating 98% of the possible matches thus reducing the amount of work needed for manual inspection. Indeed, experts that reviewed the results have identified some positive matches as potentially true and referred them for further investigation.

scholarly journals Path homology theory of edge-colored graphs

2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska
Keyword(s):  
Spectral Sequence ◽  
Edge Coloring ◽  
Homology Theory ◽  
Homotopy Category ◽  
Homology Groups ◽  
Colored Graphs ◽  
Natural Filtration ◽  
Definition Of ◽  
Exact Sequences

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.

Edge Coloring and the Möbius Strip

2021 ◽  
Vol 94 (2) ◽  
pp. 113-117
Author(s):  
Jimmy Dillies
Keyword(s):  
Edge Coloring ◽  
Möbius Strip ◽  
Mobius Strip
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