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Neighbor sum distinguishing list total coloring of IC-planar graphs without 5-cycles

Donghan Zhang (2022)

Czechoslovak Mathematical Journal

Let G = ( V ( G ) , E ( G ) ) be a simple graph and E G ( v ) denote the set of edges incident with a vertex v . A neighbor sum distinguishing (NSD) total coloring φ of G is a proper total coloring of G such that ∑ z ∈ E G ( u ) ∪ { u } φ ( z ) ≠ ∑ z ∈ E G ( v ) ∪ { v } φ ( z ) for each edge u v ∈ E ( G ) . Pilśniak and Woźniak asserted in 2015 that each graph with maximum degree Δ admits an NSD total ( Δ + 3 ) -coloring. We prove that the list version of this conjecture holds for any IC-planar graph with Δ ≥ 11 but without 5 -cycles by applying the Combinatorial Nullstellensatz.

Neochromatica

Panagiotis Cheilaris, Ernst Specker, Stathis Zachos (2010)

Commentationes Mathematicae Universitatis Carolinae

We create and discuss several modifications to traditional graph coloring. In particular, we classify various notions of coloring in a proper hierarchy. We concentrate on grid graphs whose colorings can be represented by natural number entries in arrays with various restrictions.

Netted matrices.

Stănică, Pantelimon (2003)

International Journal of Mathematics and Mathematical Sciences

Network tomography.

Berenstein, Carlos A., Gavilánez, Franklin (2007)

Revista Colombiana de Matemáticas

New Binary Extremal Self-Dual Codes of Lengths 50 and 52

Buyuklieva, Stefka (1999)

Serdica Mathematical Journal

* This work was partially supported by the Bulgarian National Science Fund under Contract No. MM – 503/1995.New extremal binary self-dual codes of lengths 50 and 52 are constructed. Some of them are the first known codes with such weight enumerators. The structure of their automorphisms groups are shown.

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