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On f-colorings of the corona product of cycles with some other graphs
Adiwijayaa,b, Salman A.N.M.a, Suprijanto D.a, Baskoro E.T.a
a Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (ITB), Indonesia
b Faculty of Science, Institut Teknologi Telkom (IT Telkom), India
[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]Let G = (V(G),E(G)) be a simple graph and / be a function from V(G) to a subset of positive integers. An f-coloring of G is a generalized edge-coloring such that every vertex v ∈ V(G) has at most f(v) edges colored with a same color. The minimum number of colors needed to define an f-coloring of G is called an /- chromatic index of G, and denoted by x’f(G)- The /-chromatic index of G is equal to Δj(G) or Δj(G) + 1, where Δj(G) = max{\d(v)/f(v)] | v ∈ V(G)}. G is called in the class-1, denoted by Cfl, if xf{G) = Δj(G) ; otherwise G is called in the class-S, denoted by Cf2. In this paper, we showed that the corona product of a cycle with either the complement of a complete graph, or a path, or a cycle is in Cfl.[/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]Chromatic index,Class-S,Complete graphs,Edge coloring,F-coloring,Positive integers[/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]Corona product,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][/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]