… The literature on the similar problem for total coloring is void. In … a graph G *K 2 is uniquely
total colorable, then X"(G) = LI + 1. Our results support the following conjecture: empty graphs, …

… We prove that if G is a UTC graph of order n and in the proper total coloring of G, there
exists a … Uniquely total colorable graphs Graphs Combin., 13 (1997), pp. 305-314 …

… all uniquely 2–list colorable graphs. In Section 3 some applications of uniquely 2–list colorable
graphs … But the union of all the lists given above, has (2k − 1) colors in total. So vertices in …

… A graph G is called uniquely vertex colorable if V(G) can be partitioned into χ(G) …
Uniquely total colorable graphs We note that a graph G is called uniquely total colorable if V(G)∪E(G) …

… We extend the concept of uniquely colorable graphs and say that a graph G is χ -iso-unique …
First, we prove some general properties about degrees of vertices of χ -iso-unique graphs G …

… A uniquely vertex-A;-colorable graph G is said to be uniquely edge-critical if for every edge
… a 2—connected graph is a function w : E(G) —> {1, 2} such that the total weight of each edge …

… introduced list coloring with the intention to study total coloring, while Erdös, Rubin and …
uniquely list colorable graphs and their relation with choosability. Consider a graph G with a …

… Then we claim that the graph is uniquely 3-colorable. If not, then let ψ be a proper 3-… Fix
ε = (ε1,ε2,...,εk) and let B(n,k, ε) be the total number of proper k-colorings on n vertices with the …

… a graph is uniquely 2{list colorable if and only if one of its blocks is not a cycle, a complete
graph, or a complete bipartite graph. … we introduce a uniquely k{list colorable graph for each k. …

… In this paper we construct uniquely (m, k)~-colourable graphs (for all positive integers m and
… uniquely (m, k)~-colourable graphs presented in this paper requires k - r-saturated graphs …