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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 ...
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 ...
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 ...
Some Families of Tree Are Elegant
(Advances in Mathematics: Scientific Journal 9, 2020-12-04)
An elegant labeling on the graph G with n vertex and m edge is a
one-to-one mapping (injection function) of the vertex set V (G) to the set of non
negative integers {0, 1, 2, 3, . . . , m} such that each edge gets the ...
An Inclusive Local Irregularity Coloring of Graphs
(Advances in Mathematics: Scientific Journal, 2020)
All graph in this paper are connected and simple. Let G = (V, E) be a simple graph, where V (G) is vertex set and E(G) is edge set. The local irregularity vertex coloring of G is l : V (G) → {1, 2, · · · , k} and w : V (G) ...