Bull. Malays. Math. Sci. Soc.

2015

DOI: 10.1007/s40840-015-0207-0

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Neighbor Sum Distinguishing Edge Colorings of Graphs with Small Maximum Average Degree

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Abstract: A proper edge-k

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Cited by 8 publications

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“…Later, Gao et al [9] showed that if G is a normal graph with ( ) [11] proved that if G is a normal graph with ( )…”

Section: Introductionmentioning

confidence: 99%

Neighbor Sum Distinguishing Index of Graphs with Maximum Average Degree

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2021

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A proper k-edge coloring of a graph)no two adjacent edges receive the same color. A neighbor sum distinguishing k-edge coloring of G is a proper k-edge coloring of G such that ( ) ( ) u e v e c e c e ∈ ∈ ≠ ∑ ∑ for each edge ( ) uv E G ∈ . The 37 12 mad G < . Our approach is based on the discharging method and Combinatorial Nullstellensatz.

“…Later, Gao et al [9] showed that if G is a normal graph with ( ) [11] proved that if G is a normal graph with ( )…”

Section: Introductionmentioning

confidence: 99%

Neighbor Sum Distinguishing Index of Graphs with Maximum Average Degree

Sun¹

2021

View full text Add to dashboard Cite

A proper k-edge coloring of a graph)no two adjacent edges receive the same color. A neighbor sum distinguishing k-edge coloring of G is a proper k-edge coloring of G such that ( ) ( ) u e v e c e c e ∈ ∈ ≠ ∑ ∑ for each edge ( ) uv E G ∈ . The 37 12 mad G < . Our approach is based on the discharging method and Combinatorial Nullstellensatz.

On the Neighbour Sum Distinguishing Index of Graphs with Bounded Maximum Average Degree

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2017

Graphs and Combinatorics

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A proper edge k-colouring of a graph G = (V, E) is an assignment c : E → {1, 2, . . . , k} of colours to the edges of the graph such that no two adjacent edges are associated with the same colour. A neighbour sum distinguishing edge k-colouring, or nsd k-colouring for short, is a proper edge k-colouring such that e∋u c(e) = e∋v c(e) for every edge uv of G. We denote by χ ′ (G) the neighbour sum distinguishing index of G, which is the least integer k such that an nsd k-colouring of G exists.

Neighbor sum distinguishing colorings of graphs with maximum average degree less than $$\tfrac{{37}} {{12}}$$3712

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2017

Acta. Math. Sin.-English Ser.

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