New upper bounds on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>L</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-labeling of the skew and converse skew product graphs

Duan, Ziming; Lv, Pingli; Miao, Lianying; Zhang, Miao; Wang, Cuiqi

doi:10.1016/j.tcs.2011.01.031

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…In [5] Ziming Duan, et al considered the skew product and the converse skew product for L(2, 1) -labeling. They obtained upper bounds for the L(2, 1) -labeling number, which improves the upper bound obtained by Shao and Zhang [17] in many cases.…”

Section: Skew Product and Converse Skew Productmentioning

confidence: 99%

Total coloring conjecture on certain classes of product graphs

Somasundaram¹,

Geetha²,

Vignesh³

2023

EJGTA

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A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph G, denoted by χ ′′ (G), is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, ∆(G) + 1 ≤ χ ′′ (G) ≤ ∆(G) + 2, where ∆(G) is the maximum degree of G. In this paper, we prove the Behzad and Vizing conjecture for Indu -Bala product graph, Skew and Converse Skew product graph, Cover product graph, Clique cover product graph and Comb product graph.

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Section: Skew Product and Converse Skew Productmentioning

confidence: 99%

Total coloring conjecture on certain classes of product graphs

Somasundaram¹,

Geetha²,

Vignesh³

2023

EJGTA

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The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

Calamoneri

2011

The Computer Journal

160

104

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Given any fixed nonnegative integer values h and k, the L(h, k)labelling problem consists in an assignment of nonnegative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with minimum span. The L(h, k)-labelling problem has been intensively studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach. It is an update of a previous survey written by the same author.

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New upper bounds on the L(2,1)-labeling of the skew and converse skew product graphs

Cited by 2 publications

References 18 publications

Total coloring conjecture on certain classes of product graphs

Total coloring conjecture on certain classes of product graphs

The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

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