2 research outputs found
Equitable neighbour-sum-distinguishing edge and total colourings
With any (not necessarily proper) edge -colouring
of a graph ,one can associate a
vertex colouring given by .A neighbour-sum-distinguishing edge -colouring is an edge
colouring whose associated vertex colouring is proper.The
neighbour-sum-distinguishing index of a graph is then the smallest for
which admitsa neighbour-sum-distinguishing edge -colouring.These notions
naturally extends to total colourings of graphs that assign colours to both
vertices and edges.We study in this paper equitable
neighbour-sum-distinguishing edge colourings andtotal colourings, that is
colourings for whichthe number of elements in any two colour classes
of differ by at most one.We determine the equitable
neighbour-sum-distinguishing indexof complete graphs, complete bipartite graphs
and forests,and the equitable neighbour-sum-distinguishing total chromatic
numberof complete graphs and bipartite graphs