Star coloring under some graph operations

2021 ◽  
pp. 2250079
Author(s):  
B. Akhavan Mahdavi ◽  
M. Tavakoli ◽  
F. Rahbarnia ◽  
Alireza Ashrafi
Keyword(s):  
Chromatic Number ◽  
Lexicographic Product ◽  
Proper Coloring ◽  
Sharp Bounds ◽  
Graph Operations ◽  
Join Of Graphs ◽  
Star Coloring ◽  
Product Of Graphs

A star coloring of a graph [Formula: see text] is a proper coloring of [Formula: see text] such that no path of length 3 in [Formula: see text] is bicolored. In this paper, the star chromatic number of join of graphs is computed. Some sharp bounds for the star chromatic number of corona, lexicographic, deleted lexicographic and hierarchical product of graphs together with a conjecture on the star chromatic number of lexicographic product of graphs are also presented.

scholarly journals HF-Index and Y-Index of Some New Graph of Operations

2022 ◽  
pp. 28-33
Author(s):  
Dr. S. Nagarajan ◽  
◽  
G. Kayalvizhi ◽  
G. Priyadharsini ◽  
◽  
...  
Keyword(s):  
Cartesian Product ◽  
Graph Operations ◽  
Join Of Graphs ◽  
Product Of Graphs ◽  
Corona Product

In this paper we derive HF index of some graph operations containing join, Cartesian Product, Corona Product of graphs and compute the Y index of new operations of graphs related to the join of graphs.

scholarly journals Sharp Bounds on the Augmented Zagreb Index of Graph Operations

2020 ◽  
Vol 44 (4) ◽  
pp. 509-522
Author(s):  
N. DEHGARDI ◽  
H. ARAM
Keyword(s):  
Simple Graph ◽  
Connectivity Index ◽  
Regular Graphs ◽  
Zagreb Index ◽  
Sharp Bounds ◽  
Graph Operations ◽  
Degree Of A Vertex ◽  
Augmented Zagreb Index ◽  
Composition Product ◽  
Product Of Graphs

Let G be a finite and simple graph with edge set E(G). The augmented Zagreb index of G is ( ) ∑ dG (u )dG (v) 3 AZI (G ) = ---------------------- , dG (u ) + dG (v) − 2 uv∈E(G ) where dG(u) denotes the degree of a vertex u in G. In this paper, we give some bounds of this index for join, corona, cartesian and composition product of graphs by general sum-connectivity index and general Randić index and compute the sharp amount of that for the regular graphs.

scholarly journals On Semitotal k-Fair and Independent k-Fair Domination in Graphs

2020 ◽  
Vol 13 (4) ◽  
pp. 779-793
Author(s):  
Marivir Ortega ◽  
Rowena Isla
Keyword(s):  
Positive Integer ◽  
Domination Number ◽  
Cartesian Product ◽  
Lexicographic Product ◽  
Dominating Sets ◽  
Sharp Bounds ◽  
Cartesian Product Of Graphs ◽  
Domination In Graphs ◽  
Product Of Graphs

In this paper, we introduce and investigate the concepts of semitotal k-fair domination and independent k-fair domination, where k is a positive integer. We also characterize the semitotal 1-fair dominating sets and independent k-fair dominating sets in the join, corona, lexicographic product, and Cartesian product of graphs and determine the exact value or sharp bounds of the corresponding semitotal 1-fair domination number and independent k-fair domination number.

scholarly journals The b-chromatic number of power graphs

2003 ◽  
Vol Vol. 6 no. 1 ◽  
Author(s):  
Brice Effantin ◽  
Hamamache Kheddouci
Keyword(s):  
Chromatic Number ◽  
Binary Trees ◽  
Proper Coloring ◽  
Power Cycles ◽  
International Audience

International audience The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x_i adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. In this paper, we discuss the b-chromatic number of some power graphs. We give the exact value of the b-chromatic number of power paths and power complete binary trees, and we bound the b-chromatic number of power cycles.

scholarly journals Another H-super magic decompositions of the lexicographic product of graphs

2018 ◽  
Vol 2 (2) ◽  
pp. 72
Author(s):  
H Hendy ◽  
Kiki A. Sugeng ◽  
A.N.M Salman ◽  
Nisa Ayunda
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Graph Decomposition ◽  
Graph Labeling ◽  
Sufficient Condition ◽  
Lexicographic Product ◽  
Simple Graphs ◽  
Product Of Graphs

<p>Let <span class="math"><em>H</em></span> and <span class="math"><em>G</em></span> be two simple graphs. The concept of an <span class="math"><em>H</em></span>-magic decomposition of <span class="math"><em>G</em></span> arises from the combination between graph decomposition and graph labeling. A decomposition of a graph <span class="math"><em>G</em></span> into isomorphic copies of a graph <span class="math"><em>H</em></span> is <span class="math"><em>H</em></span>-magic if there is a bijection <span class="math"><em>f</em> : <em>V</em>(<em>G</em>) ∪ <em>E</em>(<em>G</em>) → {1, 2, ..., ∣<em>V</em>(<em>G</em>) ∪ <em>E</em>(<em>G</em>)∣}</span> such that the sum of labels of edges and vertices of each copy of <span class="math"><em>H</em></span> in the decomposition is constant. A lexicographic product of two graphs <span class="math"><em>G</em><sub>1</sub></span> and <span class="math"><em>G</em><sub>2</sub>, </span> denoted by <span class="math"><em>G</em><sub>1</sub>[<em>G</em><sub>2</sub>], </span> is a graph which arises from <span class="math"><em>G</em><sub>1</sub></span> by replacing each vertex of <span class="math"><em>G</em><sub>1</sub></span> by a copy of the <span class="math"><em>G</em><sub>2</sub></span> and each edge of <span class="math"><em>G</em><sub>1</sub></span> by all edges of the complete bipartite graph <span class="math"><em>K</em><sub><em>n</em>, <em>n</em></sub></span> where <span class="math"><em>n</em></span> is the order of <span class="math"><em>G</em><sub>2</sub>.</span> In this paper we provide a sufficient condition for <span class="math">$\overline{C_{n}}[\overline{K_{m}}]$</span> in order to have a <span class="math">$P_{t}[\overline{K_{m}}]$</span>-magic decompositions, where <span class="math"><em>n</em> &gt; 3, <em>m</em> &gt; 1, </span> and <span class="math"><em>t</em> = 3, 4, <em>n</em> − 2</span>.</p>

scholarly journals ON DYNAMIC COLORING OF WEB GRAPH

2018 ◽  
Vol 5 (2) ◽  
pp. 11-15
Author(s):  
Aaresh R.R ◽  
Venkatachalam M ◽  
Deepa T
Keyword(s):  
Chromatic Number ◽  
Line Graph ◽  
Proper Coloring ◽  
Total Graph ◽  
Web Graph ◽  
Middle Graph

Dynamic coloring of a graph G is a proper coloring. The chromatic number of a graph G is the minimum k such that G has a dynamic coloring with k colors. In this paper we investigate the dynamic chromatic number for the Central graph, Middle graph, Total graph and Line graph of Web graph Wn denoted by C(Wn), M(Wn), T(Wn) and L(Wn) respectively.

scholarly journals On r-dynamic coloring of comb graphs

2021 ◽  
Vol 27 (2) ◽  
pp. 191-200
Author(s):  
K. Kalaiselvi ◽  
◽  
N. Mohanapriya ◽  
J. Vernold Vivin ◽  
◽  
...  
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Upper Bound ◽  
Line Graph ◽  
Proper Coloring ◽  
Total Graph ◽  
Middle Graph ◽  
Different Color

An r-dynamic coloring of a graph G is a proper coloring of G such that every vertex in V(G) has neighbors in at least $\min\{d(v),r\}$ different color classes. The r-dynamic chromatic number of graph G denoted as $\chi_r (G)$, is the least k such that G has a coloring. In this paper we obtain the r-dynamic chromatic number of the central graph, middle graph, total graph, line graph, para-line graph and sub-division graph of the comb graph $P_n\odot K_1$ denoted by $C(P_n\odot K_1), M(P_n\odot K_1), T(P_n\odot K_1), L(P_n\odot K_1), P(P_n\odot K_1)$ and $S(P_n\odot K_1)$ respectively by finding the upper bound and lower bound for the r-dynamic chromatic number of the Comb graph.

scholarly journals On the set chromatic number of the join and comb product of graphs

2020 ◽  
Vol 1538 ◽  
pp. 012009
Author(s):  
B C L Felipe ◽  
A D Garciano ◽  
M A C Tolentino
Keyword(s):  
Chromatic Number ◽  
Product Of Graphs
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