TY  - JOUR
ID  - MozafariNia2023
LB  - MozafariNia2023
AU  - Mozafari-Nia, Mahsa
AU  - Iradmusa, Moharram N.
TI  - On incidence coloring of graph fractional powers
ST  - On incidence coloring of graph fractional powers
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 1
SP  - 109
EP  - 123
DO  - https://doi.org/10.7494/OpMath.2023.43.1.109
UR  - https://doi.org/10.7494/OpMath.2023.43.1.109
AB  - For any \(n\in \mathbb{N}\), the \(n\)-subdivision of a graph \(G\) is a simple graph \(G^\frac{1}{n}\) which is constructed by replacing each edge of \(G\) with a path of length \(n\). The \(m\)-th power of \(G\) is a graph, denoted by \(G^m\), with the same vertices of \(G\), where two vertices of \(G^m\) are adjacent if and only if their distance in \(G\) is at most \(m\). In [M.N. Iradmusa, On colorings of graph fractional powers, Discrete Math. 310 (2010), no. 10-11, 1551-1556] the \(m\)-th power of the \(n\)-subdivision of \(G\), denoted by \(G^{\frac{m}{n}}\) is introduced as a fractional power of \(G\). The incidence chromatic number of \(G\), denoted by \(\chi_i(G)\), is the minimum integer \(k\) such that \(G\) has an incidence \(k\)-coloring. In this paper, we investigate the incidence chromatic number of some fractional powers of graphs and prove the correctness of the incidence coloring conjecture for some powers of graphs.
KW  - incidence coloring
KW  - incidence chromatic number
KW  - subdivision of graph
KW  - power of graph
SN  - 1232-9274
ER  -