Some properties of stepwise irregular graphs
K.G. Subramanian (kgsmani1948@gmail.com)
Graphs in which the absolute difference between the degrees of any two adjacent vertices is exactly one, are called stepwise irregular (SI) graphs. We establish several properties of SI graphs. In particular, we show that SI graphs of different order and cyclomatic numbers can be constructed from an SI graph with a vertex of degree 1 or 2. Necessary conditions and sufficient conditions for a degree sequence to be SI graphic are obtained. Moreover, a necessary condition comparing the sum of the t