Neighbor product distinguishing total colorings
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DOI: 10.1007/s10878-015-9952-0
Abstract: A total-[k]-coloring of a graph G is a mapping $$\phi : V (G) \cup E(G)\rightarrow \{1, 2, \ldots , k\}$$ϕ:V(G)∪E(G)→{1,2,…,k} such that any two adjacent elements in $$V (G) \cup E(G)$$V(G)∪E(G) receive different colors. Let… read more here.
Keywords: product distinguishing; neighbor product; distinguishing total; prime prime ... See more keywords
Neighbor sum distinguishing total coloring of 2-degenerate graphs
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DOI: 10.1007/s10878-016-0053-5
Abstract: A proper k-total coloring of a graph G is a mapping from $$V(G)\cup E(G)$$V(G)∪E(G) to $$\{1,2,\ldots ,k\}$${1,2,…,k} such that no two adjacent or incident elements in $$V(G)\cup E(G)$$V(G)∪E(G) receive the same color. Let f(v) denote… read more here.
Keywords: total coloring; sigma delta; sum distinguishing; distinguishing total ... See more keywords
The adjacent vertex distinguishing total chromatic numbers of planar graphs with $$\Delta =10$$Δ=10
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DOI: 10.1007/s10878-016-9995-x
Abstract: A (proper) total-k-coloring of a graph G is a mapping $$\phi : V (G) \cup E(G)\mapsto \{1, 2, \ldots , k\}$$ϕ:V(G)∪E(G)↦{1,2,…,k} such that any two adjacent elements in $$V (G) \cup E(G)$$V(G)∪E(G) receive different colors.… read more here.
Keywords: vertex distinguishing; distinguishing total; adjacent vertex; delta ... See more keywords