منابع مشابه
On almost distance-regular graphs
Distance-regular graphs have been a key concept in Algebraic Combinatorics and have given place to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study ‘almost distance-regular graphs’. We use this name informally for graphs that share some regularity properties that are related to distance in the ...
متن کاملAlmost-bipartite distance-regular graphs with the Q-polynomial property
Let Γ denote a Q-polynomial distance-regular graph with diameter D ≥ 4. Assume that the intersection numbers of Γ satisfy ai = 0 for 0 ≤ i ≤ D − 1 and aD 6= 0. We show that Γ is a polygon, a folded cube, or an Odd graph.
متن کاملEdge-distance-regular graphs are distance-regular
A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph Γ is distance-regular and homogeneous. More precisely, Γ is edge-distance-regular if and only if it is bipartite distance-reg...
متن کاملOn maximum matchings in almost regular graphs
In 2010, Mkrtchyan, Petrosyan and Vardanyan proved that every graph G with 2 ≤ δ(G) ≤ ∆(G) ≤ 3 contains a maximum matching whose unsaturated vertices do not have a common neighbor, where ∆(G) and δ(G) denote the maximum and minimum degrees of vertices in G, respectively. In the same paper they suggested the following conjecture: every graph G with ∆(G)− δ(G) ≤ 1 contains a maximum matching whos...
متن کاملRegular subgraphs of almost regular graphs
Suppose every vertex of a graph G has degree k or k + 1 and at least one vertex has degree k + 1. It is shown that if k > 2q 2 and q is a prime power then G contains a q-regular subgraph (and hence an r-regular subgraph for all r < q. r = q (mod 2)). It is also proved that every simple graph with maximal degree A > 2q 2 and average degree d > ((2q 2)/(2q l))(A + 1), where q is a prime power, co...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2010.10.005