Total Idempotent Graphs

8th International Conference on Current Scenario in Pure and Applied Mathematics, Tamil Nadu, Hindistan, 17 - 18 Şubat 2025, ss.3, (Özet Bildiri)

The omega invariant was introduced in 2018 to observe many graph theoretic,

algebraic, combinatoric and topological properties of all realizations of a given degree

sequence or of any given graph. It is directly related to the Euler characteristic and

the cyclomatic number of the graphs. The observed properties include cyclicity,

connectivity, numbers of components, multiple edges, loops, cycles, chords, pendant

and support vertices, etc. Since 2019, several applications of this invariant have

been found. In this work, we shall recall the omega invariant together with some

fundamental combinatoric properties and also apply it to study the constructive

properties of idempotent total graphs as algebraic graphs.