圈与路的点被多重集可区别的E-全染色OA北大核心CSTPCD

An E-total coloring of a graph G is an assignment of several colors to all vertices and edges of G such that no two adjacent vertices receive the same color and no edge receive the same color as one of its endpoints.If f is an E-total coloring of a graph G,the multiple color set of a vertex x of G under f is the multiple set composed of colors of x and the edges incident with x.If any two distinct vertices of G have distinct multiple color sets under an E-total coloring f of a graph G,then f is called an E-total coloring of G vertex-distinguished by multiple sets.An E-total chromatic number of G vertex-distinguished by multiple sets is the minimum number of the colors required in an E-total coloring of G vertex-distinguished by multiple sets.The E-total colorings of cycles and paths vertex-distinguished by multiple sets are discussed by use of the method of contradiction and the construction of concrete coloring.The optimal E-total colorings of cycles and paths vertex-distinguished by multiple sets are given and the E-total chromatic numbers of cycles and paths vertex-distinguished by multiple sets are determined in this paper.