Adjacent strong edge coloring of graphs

Zhong-fu, Zhang; Liu, Linzhong; Wang, Jianfang

doi:10.1016/s0893-9659(02)80015-5

Cited by 203 publications

(142 citation statements)

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“…The obtained proper [8]-coloring v of G is nsd, since S(x) ∩ S(y) = {v(x y)} and S(x) \ {v(x y)} = S(y) \ {v(x y)} whenever vertices x, y are adjacent in G.…”

Section: Theorem 14 If G Is a 3-regular Graph Then Ndi (G) ≤mentioning

confidence: 99%

“…This invariant has been introduced by Zhang et al [8]. It is easy to see that ndi(C 5 ) = 5 and in [8] it is conjectured that ndi(G) ≤ (G)+2 for any connected graph G = C 5 on n ≥ 3 vertices.…”

mentioning

confidence: 98%

“…It is easy to see that ndi(C 5 ) = 5 and in [8] it is conjectured that ndi(G) ≤ (G)+2 for any connected graph G = C 5 on n ≥ 3 vertices. The conjecture has been confirmed by Balister et al [3] for bipartite graphs and for graphs G with (G) = 3.…”

mentioning

confidence: 99%

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Neighbor Sum Distinguishing Index

Flandrin

Marczyk

Przybyło

et al. 2012

Graphs and Combinatorics

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We consider proper edge colorings of a graph G using colors of the set {1, . . . , k}. Such a coloring is called neighbor sum distinguishing if for any pair of adjacent vertices x and y the sum of colors taken on the edges incident to x is different from the sum of colors taken on the edges incident to y. The smallest value of k in such a coloring of G is denoted by ndi (G). In the paper we conjecture that for any connected graph G = C 5 of order n ≥ 3 we have ndi (G) ≤ (G) + 2. We prove this conjecture for several classes of graphs. We also show that ndi (G) ≤ 7 (G)/2 for any graph G with (G) ≥ 2 and ndi (G) ≤ 8 if G is cubic.

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“…The obtained proper [8]-coloring v of G is nsd, since S(x) ∩ S(y) = {v(x y)} and S(x) \ {v(x y)} = S(y) \ {v(x y)} whenever vertices x, y are adjacent in G.…”

Section: Theorem 14 If G Is a 3-regular Graph Then Ndi (G) ≤mentioning

confidence: 99%

mentioning

confidence: 98%

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Neighbor Sum Distinguishing Index

Flandrin

Marczyk

Przybyło

et al. 2012

Graphs and Combinatorics

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“…In [1], some conditional coloring problems as introduced. Some network problem can be converted to the strong edge coloring [2−5] and adjacent strong edge coloring [6] . DEFINITION 1 [2−5] For a graph G(V, E), if a proper coloring f is satisfied with [6] .Where …”

Section: Introductionmentioning

confidence: 99%

“…exist a prerfect matching 4 ; M exist a prerfect matching 6 ; M So f is a 9 − ASEECof 6 6 C C . Similarly we can proof …”

mentioning

confidence: 99%

On the Adjacent Strong Equitable Edge Coloring ofP_n∨P_n,P_n∨C_nandC_n∨C_n

Liu¹,

Zhao²,

Yao

et al. 2016

MATEC Web of Conferences

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On Neighbor-Distinguishing Index of Planar Graphs

Horňák¹,

Huang

Wang

2013

J. Graph Theory

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A proper edge coloring of a graph G without isolated edges is neighbor‐distinguishing if any two adjacent vertices have distinct sets consisting of colors of their incident edges. The neighbor‐distinguishing index of G is the minimum number ndi(G) of colors in a neighbor‐distinguishing edge coloring of G. Zhang, Liu, and Wang in 2002 conjectured that ndi (G)≤Δ(G)+2 if G is a connected graph of order at least 6. In this article, the conjecture is verified for planar graphs with maximum degree at least 12.

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Adjacent strong edge coloring of graphs

Cited by 203 publications

References 0 publications

Neighbor Sum Distinguishing Index

Neighbor Sum Distinguishing Index

On the Adjacent Strong Equitable Edge Coloring ofP_n∨P_n,P_n∨C_nandC_n∨C_n

On Neighbor-Distinguishing Index of Planar Graphs

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Adjacent strong edge coloring of graphs

Cited by 203 publications

References 0 publications

Neighbor Sum Distinguishing Index

Neighbor Sum Distinguishing Index

On the Adjacent Strong Equitable Edge Coloring ofPn∨Pn,Pn∨CnandCn∨Cn

On Neighbor-Distinguishing Index of Planar Graphs

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On the Adjacent Strong Equitable Edge Coloring ofP_n∨P_n,P_n∨C_nandC_n∨C_n