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Some graphs in Cf2 based on f-coloring
Adiwijayaa, Salman A.N.M.b, Serra O.c, Suprijanto D.b, Baskoro E.T.b
a Telkom University, Bandung, 40257, India
b Bandung Institute of Technology, Bandung, 40132, India
c Universitat Politècnica de Catalunya (UPC), Barcelona, E-08034, Spain
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2015 Academic Publications, Ltd.Let G = (V,E) be a graph and f : V → Z+a positive integer be a function. An f-coloring of G is a coloring of the edges such that every vertex ν ∈ V is incident to at most f(ν) edges of the same color. The minimum number of colors of an f-coloring of G is the f-chromatic index χ′f(G) of G. Based on the f-chromatic index, a graph G can be either in class Cf1, if χ′f(G) = Δf(G), or in class Cf2, if χ′f(G) = Δf(G)+1, where Δf(G) = maxx∈V ⌈d(ν)/f(ν)⌉. In this paper, we give some sufficient conditions for a graph to be in Cf2. One of the results is a generalization of a theorem by Zhang et al. (2008). Moreover, we show that, when f is constant and a divisor of (n-1), a maximal subgraph of the complete graph Kn which is in class Cf1 has precisely (2n) – Δf(Kn)/2 edges.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Edge coloring,F-chromatic index,F-coloring[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.12732/ijpam.v102i2.3[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]