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On incidence coloring of graph fractional powers

Mozafari-Nia Mahsa, Iradmusa Moharram N.

Opuscula Mathematica

2023

Vol. 43, no. 1

109--123

For any n ∈ N, the n-subdivision of a graph G is a simple graph G 1n 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 Gm, with the same vertices of G, where two vertices of Gm 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 Gm n is introduced as a fractional power of G. The incidence chromatic number of G, denoted by χi(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.

Subdivision of hypergraphs and their colorings

Iradmusa Moharram N.

Opuscula Mathematica

2020

Vol. 40, no. 2

271--290

In this paper we introduce the subdivision of hypergraphs, study their properties and parameters and investigate their weak and strong chromatic numbers in various cases.