Browsing Department of Mathematics by Author "Donnie Munyao Kasyoki, Paul Odhiambo Oleche"

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4-Regular prime graphs of nonsolvable groups

Donnie Munyao Kasyoki, Paul Odhiambo Oleche (CORNELL UNIVERSITY, 2019-01-11)

Let G be a finite group and cd(G) denote the character degree set for G. The prime graph ∆(G) is a simple graph whose vertex set consists of prime divisors of elements in cd(G), denoted ρ(G). Two primes p, q ∈ ρ(G) are ...
On Regular Prime Graphs of Solvable Groups

Donnie Munyao Kasyoki, Paul Odhiambo Oleche (Hikari Ltd, 2016)

Let G be a finite solvable group and∆(G) be the prime vertex graph on cd (G). We show that if∆(G) is noncomplete and regular, then G is the direct product of groups with disconnected graphs of 2 vertices.