Suhadi Wido Saputro

The metric dimension of the lexicographic product of graphs

Abstract A set of vertices W resolves a graph G if every vertex is uniquely determined by its coordinate of distances to the vertices in W . The minimum cardinality of a resolving set of G is called the metric dimension of G . In this paper, we consider a graph which is obtained by the lexicographic product between two graphs. The lexicographic product of graphs G and H , which is denoted by G ∘ H , is the graph with vertex set V ( G ) × V ( H ) = { ( a , v ) | a ∈ V ( G ) , v ∈ V ( H ) } , where ( a , v ) is adjacent to ( b , w ) whenever a b ∈ E ( G ) , or a = b and v w ∈ E ( H ) . We give the general bounds of the metric dimension of a lexicographic product of any connected graph G and an arbitrary graph H . We also show that the bounds are sharp.

On topological integer additive set-labeling of star graphs

For integer k  ≥ 2 , let X  = {0, 1, 2, …,  k } . In this paper, we determine the order of a star graph K 1,  n of n  + 1 vertices, such that K 1,  n admits a topological integer additive set-labeling (TIASL) with respect to a set X . We also give a condition for a star graph K 1,  n such that K 1,  n is not a TIASL-graph on set X .

On size multipartite Ramsey numbers for stars versus paths and cycles

Let

On size tripartite Ramsey numbers of P3 versus mK1,n

K_{l\times t}

Fractional Metric Dimension of Tree and Unicyclic Graph

be a complete, balanced, multipartite graph consisting of

Metric Dimension for Amalgamations of Graphs

l

On fractional metric dimension of comb product graphs

partite sets and

On the partition dimension of two-component graphs

t

On The Partition Dimension of Disconnected Graphs

vertices in each partite set. For given two graphs

Local metric dimension of subgraph-amalgamation of graphs.

G_1