The Dominator Edge Coloring of Graphs
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Let G be a simple graph. A dominator edge coloring (DE-coloring) of G is a proper edge coloring in which each edge of G is adjacent to every edge of some color class (possibly its own class). The dominator edge chromatic number (DEC-number) of G is the minimum number of color classes among all dominator edge colorings of G , denoted by χ d ′ G . In this paper, we establish the bounds of the DEC-number of a graph, present the DEC-number of special graphs, and study the relationship of the DEC-number between G and the operations of G .
2013 ◽
Vol 333-335
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pp. 1452-1455
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2015 ◽
Vol 07
(04)
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pp. 1550044
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2020 ◽
Vol 12
(04)
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pp. 2050035
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2018 ◽
Vol 10
(02)
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pp. 1850018
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