TY  - JOUR
ID  - Piri2021
LB  - Piri2021
AU  - Piri, Mohammad R.
AU  - Alikhani, Saeid
TI  - Introduction to dominated edge chromatic number of a graph
ST  - Introduction to dominated edge chromatic number of a graph
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 2
SP  - 245
EP  - 257
DO  - https://doi.org/10.7494/OpMath.2021.41.2.245
UR  - https://doi.org/10.7494/OpMath.2021.41.2.245
AB  - We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph \(G\), is a proper edge coloring of \(G\) such that each color class is dominated by at least one edge of \(G\). The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by \(\chi_{dom}^{\prime}(G)\). We obtain some properties of \(\chi_{dom}^{\prime}(G)\) and compute it for specific graphs. Also examine the effects on \(\chi_{dom}^{\prime}(G)\), when \(G\) is modified by operations on vertex and edge of \(G\). Finally, we consider the \(k\)-subdivision of \(G\) and study the dominated edge chromatic number of these kind of graphs.
KW  - dominated edge chromatic number
KW  - subdivision
KW  - operation
KW  - corona
SN  - 1232-9274
ER  -