scholarly journals On the Density of Nearly Regular Graphs with a Good Edge-Labeling

2012 ◽  
Vol 26 (3) ◽  
pp. 1265-1268 ◽  
Author(s):  
Abbas Mehrabian
Keyword(s):  
Regular Graphs ◽  
Edge Labeling

scholarly journals Regular Graphs and Corona Graphs Based on Special Type of Labeling

2019 ◽  
Vol 9 (2) ◽  
pp. 2662-2664
Keyword(s):  
Regular Graphs ◽  
Corona Graphs ◽  
Edge Labeling

Here we consider the special type of labeling as lucky edge labeling for Regular graphs and corona graphs.

scholarly journals On(a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Martin Bača ◽  
Andrea Semaničová-Feňovčíková ◽  
Tao-Ming Wang ◽  
Guang-Hui Zhang
Keyword(s):  
Regular Graphs ◽  
Open Problems ◽  
Arithmetic Sequence ◽  
Bijective Mapping ◽  
Vertex Weight ◽  
Positive Integers ◽  
Edge Labeling

An(a,s)-vertex-antimagic edge labeling(or an(a,s)-VAElabeling, for short) ofGis a bijective mapping from the edge setE(G)of a graphGto the set of integers1,2,…,|E(G)|with the property that the vertex-weights form an arithmetic sequence starting fromaand having common differences, whereaandsare two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. A graph is called(a,s)-antimagic if it admits an(a,s)-VAElabeling. In this paper, we investigate the existence of(a,1)-VAE labeling for disconnected 3-regular graphs. Also, we define and study a new concept(a,s)-vertex-antimagic edge deficiency, as an extension of(a,s)-VAE labeling, for measuring how close a graph is away from being an(a,s)-antimagic graph. Furthermore, the(a,1)-VAE deficiency of Hamiltonian regular graphs of even degree is completely determined. More open problems are mentioned in the concluding remarks.

scholarly journals Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yi-Wu Chang ◽  
Shan-Pang Liu
Keyword(s):  
Complete Graphs ◽  
Regular Graphs ◽  
Real Numbers ◽  
Cartesian Products ◽  
Antimagic Labeling ◽  
Edge Labeling

An edge labeling of graph G with labels in A is an injection from E G to A , where E G is the edge set of G , and A is a subset of ℝ . A graph G is called ℝ -antimagic if for each subset A of ℝ with A = E G , there is an edge labeling with labels in A such that the sums of the labels assigned to edges incident to distinct vertices are different. The main result of this paper is that the Cartesian products of complete graphs (except K 1 ) and cycles are ℝ -antimagic.

scholarly journals Remarks on the energy of regular graphs

2016 ◽  
Vol 508 ◽  
pp. 133-145 ◽  
Author(s):  
V. Nikiforov
Keyword(s):  
Regular Graphs

scholarly journals The cyclic matching sequenceability of regular graphs

2021 ◽  
Author(s):  
Daniel Horsley ◽  
Adam Mammoliti
Keyword(s):  
Regular Graphs
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