On Equitable Irregular Graphs
2020 ◽
Vol 8
(4S4)
◽
pp. 122-124
An k−edge-weighting of a graph G = (V,E) is a map 𝝋: 𝑬(𝑮) → {𝟏,𝟐,𝟑, . . . 𝒌}, }where 𝒌 ≥ 𝟏 is an integer. Denote 𝑺𝝋(𝒗) is the sum of edge-weights appearing on the edges incident at the vertex v under𝝋 . An k-edge -weighting of G is equitable irregular if |𝑺𝝋(𝒖) − 𝑺𝝋(𝒗)| ≤ 𝟏, for every pair of adjacent vertices u and v in G. The equitable irregular strength 𝑺𝒆 (𝑮) of an equitable irregular graph G is the smallest positive integer k such that there is a k-edge weighting of G. In this paper, we discuss the equitable irregular edge-weighting for some classes of graphs
2019 ◽
Vol 9
(1S4)
◽
pp. 1093-1096
2019 ◽
Vol 9
(1S4)
◽
pp. 1014-1016
2013 ◽
Vol 1
(2)
◽
pp. 177-191
Keyword(s):
2012 ◽
Vol 34
(5)
◽
pp. 918-929
◽
2009 ◽
Vol 52
(2)
◽
pp. 267-272
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