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r-Dynamic Coloring of the Corona Product of Graphs
(Discrete Mathematics, Algorithms and Applications Vol. 12, No. 2 (2020) 2050019, 2020-01-21)
Let G = (V, E) be a graph. A proper k-coloring of graph G is r-dynamic coloring if
for every v, the neighbors of vertex v receive at least min
{
r, d(v)
}
different colors. The
minimum k such that graph G has r-dynamic ...
On The Rainbow Antimagic Connection Number of Some Wheel Related Graphs
(International Journal of Academic and Applied Research (IJAAR), Vol.3 Issue 12, December – 2019, Pages: 60-64, 2019-12-01)
All graphs in this paper is connected and simple. Let ( ) be a connected and simple graph with vertices set and
edge set . A bijection function * | ( )|+ is called an edge antimagic vertex ...
On The Packing k-Coloring of Edge Corona Product
(International Journal of Academic and Applied Research (IJAAR), Vol. 3 Issue 12, December – 2019, Pages: 55-59, 2019-12-01)
All graph in this paper is connected and simple graph. Let
du,v
be a distance between any vertex
u
and
v
in graph
G V,E
. A function
c :VG1, 2,, k
is called a packing k-coloring if every two vertices ...
The r-Dynamic Local Irregularity Vertex Coloring of Graph
(INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 07, JULY 2019, 2019-07-01)
We define the r-dynamic local irregularity vertex coloring. Suppose : V(G) {1,2, … , k} is called vertex irregular k-labeling and w : V(G)
N where 𝑤(𝑢) = ∑
(𝑣)
. is called r-dynamic local irregular vertex ...
On the Local Irregularity Vertex Coloring of Related Grid Graph
(International Journal of Academic and Applied Research (IJAAR), Vol. 4 Issue 2, February – 2020, Pages: 1-4, 2020-02-01)
All graph in this paper is connected and simple graph. Let graph d(u,v) be a distance between any vertex u and v in
graph ( ). A functio ( ) * +n is called vertex irregular k-labelling and ( ) where ...
On the r-Dynamic Chromatic Number of the Corronation by Complete Graph
(IOP Conf. Series: Journal of Physics: Conf. Series 1008 (2018) 012033, 2018-04-27)
In this paper we will study the r-dynamic chromatic number of the coronation
by complete graph. A proper k-coloring of graph G such that the neighbors of any vertex v
receive at least minfr; d(v)g di®erent colors. The ...
Metric Chromatic Number of Unicyclic Graphs
(INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 06, JUNE 2019, 2019-06-09)
All graphs in this paper are nontrivial and connected graph. Let 𝑓 ∶ 𝑉 (𝐺) → *1,2, … , 𝑘+ be a vertex coloring of a graph 𝐺where two adjacent
vertices may be colored the same color. Consider the color classes Π = ...
Local Irregular Vertex Coloring of Some Families Graph
(Journal of Discrete Mathematical Sciences and Cryptography, (DOI : 10.1080/09720529.2020.1754541), 2020-06-09)
All graph in this paper is connected and simple graph. Let d(u, v) be a distance between
any vertex u and v in graph G = (V, E ). A function : ( )
l V G
{1, 2,
, }
k
→
is called vertex irregular
k-labelling ...
Local Antimagic r-dynamic Coloring of Graphs
(IOP Conf. Series: Earth and Environmental Science 243 (2019) 012077, 2019-04-09)
Let G = (V; E) be a connected graph. A bijection function f : E(G) !
f1; 2; 3; ; E(G)jg is called a local antimagic labeling if for all uv 2 E(G)s, w(u)
6= w(v),
where w(u) = e2E(u)f(e). Such that, local antimagic ...
On the Chromatic Number Local Irregularity of Related Wheel Graph
(IOP Conf. Series: Journal of Physics: Conf. Series 1211 (2019) 012003, 2019-05-07)
A function f is called a local irregularity vertex coloring if (i) l : V (G) !
f1; 2; ; kg as vertex irregular k-labeling and w : V (G) ! N, for every uv 2 E(G); w(u)
6= w(v)
where w(u) = v2N(u)l(v) and (ii) ...