منابع مشابه
Isometric embeddings of Johnson graphs in Grassmann graphs
Let V be an n-dimensional vector space (4 ≤ n < ∞) and let Gk(V ) be the Grassmannian formed by all k-dimensional subspaces of V . The corresponding Grassmann graph will be denoted by Γk(V ). We describe all isometric embeddings of Johnson graphs J (l,m), 1 < m < l − 1 in Γk(V ), 1 < k < n − 1 (Theorem 4). As a consequence, we get the following: the image of every isometric embedding of J (n, k...
متن کاملReciprocal Degree Distance of Grassmann Graphs
Recently, Hua et al. defined a new topological index based on degrees and inverse of distances between all pairs of vertices. They named this new graph invariant as reciprocal degree distance as 1 { , } ( ) ( ( ) ( ))[ ( , )] RDD(G) = u v V G d u d v d u v , where the d(u,v) denotes the distance between vertices u and v. In this paper, we compute this topological index for Grassmann graphs.
متن کاملEmbeddings of Affine Grassmann Spaces
In this paper we prove that if a Grassmann space Δ = GrA(m,h,K) of the h–subspaces of an affine space A = AG(m,K) has an embedding e into a projective space PG(n,K′) over a skew–field K′, and e satisfies two suitable conditions (α) and (β), then K and K′ are isomorphic fields and Δ is, up to projections, an affine Grassmannian. Mathematics Subject Classification (2000). 51A45; 51M35.
متن کاملLabeling Subgraph Embeddings and Cordiality of Graphs
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$. For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...
متن کاملAccepted to Advances in Geometry CHARACTERIZATION OF ISOMETRIC EMBEDDINGS OF GRASSMANN GRAPHS
Let V be an n-dimensional left vector space over a division ring R. We write Gk(V ) for the Grassmannian formed by k-dimensional subspaces of V and denote by Γk(V ) the associated Grassmann graph. Let also V ′ be an n′-dimensional left vector space over a division ring R′. Isometric embeddings of Γk(V ) in Γk′ (V ′) are classified in [13]. A classification of J(n, k)-subsets in Gk′ (V ′), i.e. ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.11.036