The 3-rainbow index of some graphs that constructed by joining a graph with a trivial graph

Kartika, Dinda; Salman, A. N. M.

doi:10.1088/1742-6596/1127/1/012060

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first and second authors [4] investigated the rx 3 of amalgamation of some graphs of diameter 2, meanwhile Liu and Hu [17] investigated the rx 3 of three graph product operations, which are strong product, Cartesian product, and lexicographic product. Some other results about rx k of graphs can be found in [9,10,13,15,16].…”

Section: Introductionmentioning

confidence: 91%

The strong 3-rainbow index of edge-comb product of a path and a connected graph

Awanis¹,

Salman²,

Saputro³

2022

EJGTA

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 91%

The strong 3-rainbow index of edge-comb product of a path and a connected graph

Awanis¹,

Salman²,

Saputro³

2022

EJGTA

View full text Add to dashboard Cite

“…[9,10]), some authors also studied the rx 3 of some graph operations (e.g. [4,13,19]), the upper bounds for the rx 3 of graphs (e.g. [5,20]), and the characterization of graphs G with certain values of rx 3 (G) (e.g.…”

Section: Introductionmentioning

confidence: 99%

Graphs with strong 3-rainbow index equals 2

Salman

Awanis

Saputro

2022

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Let G be an edge-colored connected graph of order n ≥ 3, where adjacent edges may be colored the same. Let k be an integer with 2 ≤ k ≤ n and S ⊆ V (G) with |S| = k. The Steiner distance d(S) of S is the minimum size of a tree in G connecting S. The strong k-rainbow index srxk (G) of G is the minimum number of colors required to color the edges of G so that every set S in G is connected by a tree of size d(S) whose edges have distinct colors. We focus on k = 3. In this paper, we first characterize the graphs G with srx 3 (G) = 2. According to the definition, it is clearly that ‖G‖ is the trivial upper bound for srx 3(G). Several previous researchers have shown that there exist some connected graphs G such that srx 3(G) = ‖G‖. Hence, in this paper, we provide another graph G such that srx 3(G) = ‖G‖.

show abstract

The 3-rainbow index of some graphs that constructed by joining a graph with a trivial graph

Cited by 2 publications

References 7 publications

The strong 3-rainbow index of edge-comb product of a path and a connected graph

The strong 3-rainbow index of edge-comb product of a path and a connected graph

Graphs with strong 3-rainbow index equals 2

Contact Info

Product

Resources

About