Rinovia Simanjuntak

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.

Vertex-antimagic total labelings of graphs

In this paper we introduce a new type of graph labeling, the

Large bipartite Cayley graphs of given degree and diameter

(a, d)

Graphs of order two less than the Moore bound

- vertex-antimagic total labeling, which is a generalization of several other types of labelings. A connected graph

On Super Edge-Magic Strength and Deficiency of Graphs

G(V,E)

The Partition Dimension of a Subdivision of a Complete Graph

is said to be

Total vertex irregularity strength of trees with maximum degree five

(a, d)

Locating-chromatic number for a graph of two components

-vertex-antimagic total if there exist positive integers

Total vertex irregularity strength of trees with maximum degree four

a

The rainbow connection number of some subdivided roof graphs

,