scholarly journals Even-odd Harmonious Labeling of Some Graphs

2021 ◽  
Vol 10 (4) ◽  
pp. 149-151
Author(s):  
Dhvanik H. Zala ◽  
Narendra T. Chotaliya ◽  
Mehul A. Chaurasiya
Keyword(s):  
Bijective Mapping ◽  
Injective Mapping ◽  
Harmonious Labeling

Let G = be a graph, with and . An injective mapping is called an even-odd harmonious labeling of the graph G, if an induced edge mapping such that (i) is bijective mapping (ii) The graph acquired from this labeling is called even-odd harmonious graph. In this paper, we discovered some interesting results like H-graph, comb graph, bistar graph and graph for even-odd harmonious labeling.

scholarly journals Orthogonal labeling

2016 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Bernard Immanuel ◽  
Kiki A. Sugeng
Keyword(s):  
Euclidean Space ◽  
Early Result ◽  
Algebraic Structure ◽  
Connected Graph ◽  
Maximum Degree ◽  
Injective Mapping ◽  
Distance Magic Labeling ◽  
Harmonious Labeling ◽  
Simple Connected Graph ◽  
Cycle Graph

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>Let ∆</span><span>G </span><span>be the maximum degree of a simple connected graph </span><span>G</span><span>(</span><span>V,E</span><span>). An injective mapping </span><span>P </span><span>: </span><span>V </span><span>→ </span><span>R</span><span>∆</span><span>G </span><span>is said to be an orthogonal labeling of </span><span>G </span><span>if </span><span>uv,uw </span><span>∈ </span><span>E </span><span>implying (</span><span>P</span><span>(</span><span>v</span><span>) </span><span>− </span><span>P</span><span>(</span><span>u</span><span>)) </span><span>· </span><span>(</span><span>P</span><span>(</span><span>w</span><span>) </span><span>− </span><span>P</span><span>(</span><span>u</span><span>)) = 0, where </span><span>· </span><span>is the usual dot product defined in Euclidean space. A graph </span><span>G </span><span>which has an orthogonal labeling is called an orthogonal graph. This labeling is motivated by the existence of several labelings defined by some algebraic structure, i.e. harmonious labeling and group distance magic labeling. In this paper we study some preliminary results on orthogonal labeling. One of the early result is the fact that cycle graph with even vertices are orthogonal, while ones with odd vertices are not. The main results in this paper state that any graph containing </span><span>K</span><span>3 </span><span>as its subgraph is non-orthogonal and that a graph </span><span>G</span><span>′ </span><span>obtained from adding a pendant to a vertex in orthogonal graph </span><span>G </span><span>is orthogonal. In the end of the paper we state the corollary that any tree is orthogonal.<br /> </span></p></div></div></div>

scholarly journals On Harmonious Labeling of Corona Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Martin Bača ◽  
Maged Z. Youssef
Keyword(s):  
Harmonious Labeling ◽  
Corona Graphs

A graphGwithqedges is said to be harmonious, if there is an injectionffrom the vertices ofGto the group of integers moduloqsuch that when each edgexyis assigned the labelf(x)+f(y)(modq), the resulting edge labels are distinct. In this paper, we study the existence of harmonious labeling for the corona graphs of a cycle and a graphGand for the corona graph ofK2and a tree.

PARIKH MATRICES, AMIABILITY AND ISTRAIL MORPHISM

2010 ◽  
Vol 21 (06) ◽  
pp. 1021-1033 ◽  
Author(s):  
ADRIAN ATANASIU
Keyword(s):  
Injective Mapping ◽  
Additional Information ◽  
Binary Case ◽  
Matrix Mapping

Using the fact that the Parikh matrix mapping is not an injective mapping, the paper investigates some properties of the set of words having the same Parikh matrix; these words are called "amiable" or "M - equivalent". The presented paper uses the results obtained in [3] for the binary case. The aim is to distinguish the amiable words by using a morphism that provides additional information about them. The morphism proposed here is the Istrail morphism.

scholarly journals Pelabelan Harmonis Ganjil pada Graf Bunga Double Quadrilateral

2020 ◽  
Vol 20 (1) ◽  
pp. 12
Author(s):  
Fery Firmansah
Keyword(s):  
Research Method ◽  
Graph Labeling ◽  
New Class ◽  
Harmonious Labeling

Graf harmonis ganjil adalah graf yang memenuhi sifat-sifat pelabelan harmonis ganjil. Tujuan dari penelitian ini adalah mendapatkan kelas graf baru yang merupakan graf harmonis ganjil. Metode penelitian yang digunakan terdiri dari beberapa tahapan yaitu konstruksi definisi, formulasi fungsi pelabelan dan pembuktian teorema. Hasil dari penelitian ini adalah konstruksi graf bunga double quadrilateral  dengan  dan graf bunga variasi double quadrilateral  dengan  yang merupakan pengembangan dari graf double quadrilateral  dan graf variasi double quadrilateral . Lebih lanjut telah dibuktikan bahwa graf  dan  adalah graf harmonis ganjil.Kata Kunci: graf double quadrilateral, graf bunga, graf harmonis ganjil, pelabelan graf Odd Harmonious Labelling on The Flower Double Quadrilateral Graphs ABSTRACTOdd harmonious graphs are graphs that have odd harmonious labeling properties. The purpose of this study is to get a new class of graphs which are odd harmonious graphs. The research method used consists of several stages, namely construction of definitions, formulation of labeling functions and proof of theorems.  The results of this study is to get a graph construction will be given, namely the flower quadrilateral graphs  with  and the flower variation of quadrilateral graphs  with , which are the development of double quadrilateral graphs  and variation double quadrilateral graphs . It has further been proven that  and  are odd harmonious graphs.Keywords: double quadrilateral graph, flower graph, labeling graph, odd harmonious graph

scholarly journals Odd harmonious labeling of super subdivisión graphs

2019 ◽  
Vol 38 (1) ◽  
pp. 1-11 ◽  
Author(s):  
P. Jeyanthi ◽  
S. Philo ◽  
M. K. Siddiqui
Keyword(s):  
Harmonious Labeling

scholarly journals Prime Harmonious Labeling of Some New Graphs

2016 ◽  
Vol 12 (05) ◽  
pp. 57-61
Author(s):  
P. Deepa ◽  
S. Uma Maheswari ◽  
K. Indirani
Keyword(s):  
Harmonious Labeling

scholarly journals Odd Harmonious Labeling on Pleated of the Dutch Windmill Graphs

CAUCHY ◽  
2017 ◽  
Vol 4 (4) ◽  
pp. 161
Author(s):  
Fery Firmansah ◽  
Muhammad Ridlo Yuwono
Keyword(s):  
Harmonious Labeling

A graph G(p,q) with p=|V(G)| vertices and q=|E(G)| edges. The graph G(p,q) is said to be odd harmonious if there exist an injection f: V(G)-&gt;{0,1,2,...,2q-1} such that the induced function f*: E(G)-&gt;{1,2,3,...,2q-1} defined by  f*(uv)=f(u)+f(v) which is a bijection and f is said to be odd harmonious labeling of G(p,q). In this paper we prove that pleated of the Dutch windmill graphs C_4^(k)(r) with k&gt;=1 and r&gt;=1 are odd harmonious graph. Moreover, we also give odd harmonious labeling construction for the union pleated of the Dutch windmill graph   C_4^(k)(r) union C_4^(k)(r) with k&gt;=1 and r&gt;=1.

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