Expanding stars
A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced...
Let and be copies of a graph , and let be a function. Then a functigraph is a generalization of a permutation graph, where and . In this paper, we study colorability and planarity of functigraphs.
We define the generalized outerplanar index of a graph and give a full characterization of graphs with respect to this index.