Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 30 November 2020Accepted: 26 July 2021Published online: 18 2021Keywordscounting modulo 2, counting complexity, graph homomorphisms, parity complexity dichotomyAMS Subject Headings68Q17, 68Q25Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society...

Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.

For each $$n\ge 14$$ , we provide an example of a linklessly embeddable, Tutte-4-connected graph order n. We start with fourteen, and perform 4-vertex splittings to inductively build the family triangle free, 4-connected graphs. prove graphs constructed are as minors clique sums over $$K_4$$ embeddable

let $g$ be a non-abelian finite group. in this paper, we prove that $gamma(g)$ is $k_4$-free if and only if $g cong a times p$, where $a$ is an abelian group, $p$ is a $2$-group and $g/z(g) cong mathbb{ z}_2 times mathbb{z}_2$. also, we show that $gamma(g)$ is $k_{1,3}$-free if and only if $g cong {mathbb{s}}_3,~d_8$ or $q_8$.