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- W4376988520 abstract "Let $Gamma=(X,mathcal{R})$ denote a finite, simple, connected, and undirected non-bipartite graph with vertex set $X$ and edge set $mathcal{R}$. Fix a vertex $x in X$, and define $mathcal{R}_f = mathcal{R} setminus {yz mid partial(x,y) = partial(x,z)}$, where $partial$ denotes the path-length distance in $Gamma$. Observe that the graph $Gamma_f=(X,mathcal{R}_f)$ is bipartite. We say that $Gamma$ supports a uniform structure with respect to $x$ whenever $Gamma_f$ has a uniform structure with respect to $x$. Assume that $Gamma$ is a distance-regular graph with classical parameters $(D,q,alpha,beta)$ with $q le 1$. Recall that $q$ is an integer, which is not equal to $0$ or $-1$. The purpose of this paper is to study when $Gamma$ supports a uniform structure with respect to $x$. The main result of the paper is a complete classification of graphs with classical parameters with $qleq 1$ and $D ge 4$ that support a uniform structure with respect to $x$." @default.
- W4376988520 created "2023-05-18" @default.
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- W4376988520 date "2023-05-15" @default.
- W4376988520 modified "2023-10-11" @default.
- W4376988520 title "Distance-regular graphs with classical parameters that support a uniform structure: case $q le 1$" @default.
- W4376988520 doi "https://doi.org/10.48550/arxiv.2305.08937" @default.
- W4376988520 hasPublicationYear "2023" @default.
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