A Note on Neighbor Expanded Sum Distinguishing Index

Abstract A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = {1, . . . , k}. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction. In this paper, we consider the sum of colors on incident edges and adjacent vertices.

[1]  Florian Pfender,et al.  Vertex-coloring edge-weightings: Towards the 1-2-3-conjecture , 2010, J. Comb. Theory B.

[2]  Jakub Przybylo,et al.  On a 1, 2 Conjecture , 2010, Discret. Math. Theor. Comput. Sci..

[3]  A. Thomason,et al.  Edge weights and vertex colours , 2004 .