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Resolving Domination Numbers of Family of Tree Graph
(International Journal of Academic and Applied Research (IJAAR), Vol. 4 Issue 1, January – 2020, Pages: 27-30, 2020-01-09)
All graph in this paper are members of family of graph tree. Let G is a connected graph, for an ordered set
W={w1,w2,...,wk} of vertices and a vertex which is not element of W, then W is dominating set of graph G when the ...
On r-Dynamic Chromatic Number of the Corronation of Path and Several Graphs
(International Journal of Advanced Engineering Research and Science (IJAERS), [Vol-4, Issue-4, Apr- 2017], 2017-04-09)
This study is a natural extension of k -proper
coloring of any simple and connected graph G. By a n rdynamic
coloring of a graph G, we mean a proper k coloring
of
graph
G
such
that
the
neighbors
of
any
vert ...
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 ...
Vertex Coloring Edge-Weighting of Coronation by Path Graphs
(IOP Conf. Series: Journal of Physics: Conf. Series 1211 (2019) 012004, 2019-05-07)
In this paper, we study vertex coloring edge of corona graph. A k-edge weigting of
graph G is mapping w : (EG) ! f1; 2; ; kg. An edge-weighting w induces a vertex coloring
Fw : V (G) ! N de ned by fw(v) =
P
v2e
w(e). ...
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 ...
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 ...
The 2-Distance Chromatic Number of Some Wheel Related Graphs
(Far East Journal of Mathematical Sciences (FJMS), Volume 103, Number 3, 2018, Pages 645-657, 2018-02-09)
Let ( )EVG
, be a simple and connected graph of vertex set V and
edge set E. By the 2-distance chromatic number of a graph G, we
mean a map ( ) {
}k
c
GV
,1
,2
,3
...,
: →
such that any two vertices ...
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 ...
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 Packing k-Coloring of Unicyclic Graph Family
(International Journal of Academic and Applied Research (IJAAR), Vol. 4 Issue 1, January – 2020, Pages: 1-9, 2020-01-09)
All graph in this paper is connected graph. Let
du,v
be a distance between any vertex
u
and
v
in graph
GV,E.
A function
c :VG 1, 2, , k
is called a packing
k coloring if every two vertex of color
i
are ...