Conlon and Lee asked for strongly dominating graphs beyond norming graphs and even paths. We construct a two-parameter family of pairwise non-isomorphic $2$-connected strongly dominating graphs that are not seminorming, and hence lie outside the two classes of examples previously identified for signed strong domination. The construction uses cyclic amalgamation of two-rooted blocks. For root-reversible blocks, we characterize the generation of all even cyclic amalgams by local even-Schatten inequalities for transfer operators. We determine this criterion for $K_{2,m}$, with the roots in the part of size $m$: it holds exactly when $m$ is even. We also classify the connected outerplanar strongly dominating graphs and the connected root-reversible outerplanar blocks satisfying the universal cyclic criterion.
Domination is among the most popular topics in graph theory, both due to its combinatorial appeal and a number of practical applications. Cylindrical graphs are Cartesian products of a path and a cycle. Usually, for some special subfamilies, natural constructions exist that give exact solutions. On the other hand, in g...
In even characteristic, the first subconstituent of an orthogonal graph at a singular point is shown to be the complement of an affine polar graph. This identification yields the full automorphism group as an affine semisimilarity group and provides explicit extensions to the ambient graph. Maximum independent sets are...
The generating graph $\Gamma(G)$ of a finite group $G$ has vertex set $G\setminus\{1\}$, and two distinct vertices are adjacent if and only if they generate $G$. Breuer, Guralnick, Lucchini, Maroti and Nagy [Bull. Lond. Math. Soc. 42 (2010), 621--633] conjectured that, for every finite group $G$ with at least four elem...
We construct a family of finite local rings whose annihilating-ideal graphs are naturally described by orthogonality of subspaces of $\mathbb{F}_2^n$. For $n=4$ we determine the clique and chromatic numbers exactly and obtain \[ \omega(\AG(R_4))=5<6=\chi(\AG(R_4)). \] Thus $\AG(R_4)$ is not weakly perfect, and the Behb...
We study the number of minimal transitive factorizations of the identity permutation in $S_n$ into transpositions supported on a quasi-threshold graph. We show that this number is always divisible by $(2n-2)!/n!$, which is the factorization count for a star graph, as shown by Irving and Rattan. To prove this, we give a...
This paper utilizes an extremely simple idea: in the multiplicative group of a finite field $F_q$, cosets of a certain subgroup are considered, and an attempt is made to combine these cosets into pairs such that the resulting induced subgraph in the corresponding Paley graph is strongly regular. It is shown that there...
V. Byzov· 0 citations
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