Total rainbow connection numbers of some special graphs

Ma, Yingbin; Nie, Kairui; Jin, Fengxia; Wang, Cui

doi:10.1016/j.amc.2019.05.008

Cited by 4 publications

(1 citation statement)

References 21 publications

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“…As a natural extension, Uchizawa et al [30] and Liu et al [21] introduced the concept of total rainbow connection number, respectively. For more results, the reader can see [7], [13], [22]- [24] for details. The survey [18] and a new monograph [17] have given more results on the rainbow connectivity of graphs.…”

Section: Introductionmentioning

confidence: 99%

(Strong) Proper Connection in Some Digraphs

Nie

2019

IEEE Access

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An arc-colored digraph D is proper connected if any pair of vertices v i , v j ∈ V (D) there is a proper v i − v j path whose adjacent arcs have different colors and a proper v j − v i path whose adjacent arcs have different colors. The proper connection number of a digraph D is the minimum number of colors needed to make D proper connected, denoted by − → pc(D). An arc-colored digraph D is strong proper connected if any pair of vertices v i , v j ∈ V (D) there is a proper v i − v j geodesic and a proper v j − v i geodesic. The strong proper connection number of D is the minimum number of colors required to color the arcs of D in order to make D strong proper connected, denoted by − → spc(D). In this paper, we will show some results on − → pc(D) and − → spc(D), mostly for the case of the (strong) proper connection numbers of cacti and circulant digraphs. INDEX TERMS Proper path, proper connection number, proper geodesic, strong proper connection number.

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Section: Introductionmentioning

confidence: 99%

(Strong) Proper Connection in Some Digraphs

Nie

2019

IEEE Access

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Total-rainbow connection and forbidden subgraphs

Zhang,

Jiang,

2024

Discrete Applied Mathematics

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On rainbow antimagic coloring of special graphs

Septory

Utoyo

Dafik

et al. 2021

J. Phys.: Conf. Ser.

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Let G(V, E) be a connected, undirected and simple graph with vertex set V(G) and edge set E(G). A labeling of a graph G is a bijection f from V(G) to the set {1, 2,…, | V(G)|}. The bijection f is called rainbow antimagic vertex labeling if for any two edge uv and u’v’ in path x — y,w(uv) = w(u’v’) w(uv), where w(uv) = f (u) + f (v) and x,y ∈ V(G). A graph G is a rainbow antimagic connection if G has a rainbow antimagic labeling. Thus any rainbow antimagic labeling induces a rainbow coloring of G where the edge uv is assigned with the color w(uv). The rainbow antimagic connection number of G, denoted by rac(G), is the smallest number of colors taken over all rainbow colorings induced by rainbow antimagic labeling of G. In this paper, we show the exact value of the rainbow antimagic connection number of jahangir graph J2,m, lemon graph Lem, firecracker graph (Fm,3), complete bipartite graph (K2,m), and double star graph (Sm,m).

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Total rainbow connection numbers of some special graphs

Cited by 4 publications

References 21 publications

(Strong) Proper Connection in Some Digraphs

(Strong) Proper Connection in Some Digraphs

Total-rainbow connection and forbidden subgraphs

On rainbow antimagic coloring of special graphs

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