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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Subramanian, K.G.
Visiting Professor (Honorary) Liverpool Hope University
Electrical & Electronics Engineering

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Some properties of stepwise irregular graphs Bera, Somnath; Paul, Prithwineel; Subramanian, K.G.
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 1 (2026): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2026.14.1.14

Abstract

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 terms of a partition of SI graph and its conjugate partition is obtained. Properties of SI graphs under certain elementary graph operations are also investigated.
Co-Authors Bera, Somnath Paul, Prithwineel