International audienceWe consider proper edge colorings of a graph G using colors of the set {1, . . . , k}. Such a coloring is called neighbor sum distinguishing if for any pair of adjacent vertices x and y the sum of colors taken on the edges incident to x is different from the sum of colors taken on the edges incident to y. The smallest value of k in such a coloring of G is denoted by ndiΣ(G). In the paper we conjecture that for any connected graph G ≠ C 5 of order n ≥ 3 we have ndiΣ(G) ≤ Δ(G) + 2. We prove this conjecture for several classes of graphs. We also show that ndiΣ(G) ≤ 7Δ(G)/2 for any graph G with Δ(G) ≥ 2 and ndiΣ(G) ≤ 8 if G is cubic
A proper [k]-total coloring c of a graph G is a proper total coloring c of G using colors of the set...
For an assignment of numbers to the vertices of a graph, let S[u] be the sum of the labels of all th...
International audienceThe 1-2-3 Conjecture asks whether every graph with no connected component isom...
International audienceWe consider proper edge colorings of a graph G using colors of the set {1, . ....
International audienceWe consider proper edge colorings of a graph G using colors of the set {1, . ....
A proper total k-coloring ϕ of G with ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(z) for each uv∈E(G) is called a...
A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k]...
summary:Let $G=(V(G),E(G))$ be a simple graph and $E_{G}(v)$ denote the set of edges incident with a...
summary:Let $G=(V(G),E(G))$ be a simple graph and $E_{G}(v)$ denote the set of edges incident with a...
AbstractAn edge colouring of a graph G without isolated edges is neighbour-distinguishing if any two...
A total k-weighting f of a graph G is an assignment of integers from the set {1, . . . , k} to the v...
Let G be a graph and ϕ:V(G)∪E(G)→{1,2,3,…,k} be a k-total coloring. Let w(v) denote the sum of color...
Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually...
International audienceA d-relaxed k-edge colouring is an edge colouring using colours from the set {...
Symmetry, such as structural symmetry, color symmetry and so on, plays an important role in graph co...
A proper [k]-total coloring c of a graph G is a proper total coloring c of G using colors of the set...
For an assignment of numbers to the vertices of a graph, let S[u] be the sum of the labels of all th...
International audienceThe 1-2-3 Conjecture asks whether every graph with no connected component isom...
International audienceWe consider proper edge colorings of a graph G using colors of the set {1, . ....
International audienceWe consider proper edge colorings of a graph G using colors of the set {1, . ....
A proper total k-coloring ϕ of G with ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(z) for each uv∈E(G) is called a...
A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k]...
summary:Let $G=(V(G),E(G))$ be a simple graph and $E_{G}(v)$ denote the set of edges incident with a...
summary:Let $G=(V(G),E(G))$ be a simple graph and $E_{G}(v)$ denote the set of edges incident with a...
AbstractAn edge colouring of a graph G without isolated edges is neighbour-distinguishing if any two...
A total k-weighting f of a graph G is an assignment of integers from the set {1, . . . , k} to the v...
Let G be a graph and ϕ:V(G)∪E(G)→{1,2,3,…,k} be a k-total coloring. Let w(v) denote the sum of color...
Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually...
International audienceA d-relaxed k-edge colouring is an edge colouring using colours from the set {...
Symmetry, such as structural symmetry, color symmetry and so on, plays an important role in graph co...
A proper [k]-total coloring c of a graph G is a proper total coloring c of G using colors of the set...
For an assignment of numbers to the vertices of a graph, let S[u] be the sum of the labels of all th...
International audienceThe 1-2-3 Conjecture asks whether every graph with no connected component isom...