# Further results on partition dimension of corona products

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An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper we...

- Characterizing all graphs containing cycles with locating-chromatic number 3. Asmiati; Baskoro, Edy Tri // AIP Conference Proceedings;5/22/2012, Vol. 1450 Issue 1, p351
Let G be a connected graph G. Let c be a k-coloring of V(G) which induces an ordered partition Î = {S1,S2, ...,Sk} of V(G), where Si is the set of vertices receiving color i. The color code cÎ (Î½) of vertex Î½ is the ordered k-tuple (d(Î½,S1), d(Î½, S2), ..., d(Î½, Sk)), where...

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An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted by rc( G), is the smallest number of colors that are needed in order to make G rainbow connected. In this...

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A two-colored digraph D(2) is a digraph D whose each of its arc is colored by either red or blue. For nonnegative integers s and t with s+t > 0, an (s, t)-walk in a two-colored digraph is a walk of length s+t consisting of s red arcs and t blue arcs. The vector (s, t)T is the composition of the...

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The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. For the path Pn of length n, the crossing numbers of Cartesian products Gâ–¡Pn for all connected graphs G on five vertices are also known. In this paper, the crossing numbers...

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In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) â€” the irregular coloring number,...

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An edge-colored graph G is rainbow connected if every two vertices of G are connected by a path whose edges have distinct colors. The rainbow connection number of G, denoted by rc( G), is the minimum number of colors that are needed to make G rainbow connected. In this paper we give a...

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A facial parity edge-coloring of a $$2$$ -edge-connected plane graph is such an edge-coloring in which no two face-adjacent edges receive the same color and in addition, for each face $$f$$ and each color $$c$$ either no edge or an odd number of edges incident with $$f$$ is colored with $$c$$ ....

- On the Rainbow Coloring for Some Graph Operations. Dafik; Ika Hesti Agustin; Fajariyato, Anang; Alfarisi, Ridho // AIP Conference Proceedings;2016, Vol. 1707 Issue 1, p1
Let G = (V,E) be a nontrivial, finite, simple and undirected connected graph on which is defined a coloring f : E(G)â†’{1,2, ...,k}, k âˆˆ N. The adjacent edges may be colored the same colors. A path in an edge colored graph is said to be a rainbow path if no two edges on the path have...