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Domination Number of Vertex Amalgamation of Graphs
(2017-09-11)
For a graph G = (V, E), a subset S of V is called a dominating set if every vertex x in
V is either in S or adjacent to a vertex in S. The domination number 𝜸(𝑮) is the minimum
cardinality of the dominating set of G. ...
THE SIMILARITY OF METRIC DIMENSION AND LOCAL METRIC DIMENSION OF ROOTED PRODUCT GRAPH
(2017-09-11)
Let G be a connected graph with vertex set ( )GV and =W
{}()....,,,
⊂ The representation of a vertex ( )GVv ∈ with
respect to W is the ordered k-tuple
( ) ( ) ( )( ...,,,,,
GVwww
21
()),,
k
k
1
wvdwvdWvr ...
ON COMMUTATIVE CHARACTERIZATION OF GENERALIZED COMB AND CORONA PRODUCTS OF GRAPHS WITH RESPECT TO THE LOCAL METRIC DIMENSION
(2017-09-11)
Let G be a connected graph with vertex set ( )GV and =W
{}( )....,,,
GVwww
21
m
⊂ The representation of a vertex ( ),GVv ∈
with respect to W is the ordered m-tuple ( ) ( )( ,,
() ( )),,...,,,
2 m
wvdWvr =| ...