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9.498  Articles
1 of 951 pages  |  10  records  |  more records»
An extremal graph for a graph HH on nn vertices is a graph on nn vertices with maximum number of edges that does not contain HH as a subgraph. Let Tn,rT_{n,r} be the Turán graph, which is the complete rr-partite graph on nn vertices with part sizes that d... see more

We compute one of the distinguished extremal Betti number of the binomial edge ideal of a block graph, and classify all block graphs admitting precisely one extremal Betti number.

In this paper, the vertex-degree function index Hf(G) is considered when function f(x) belongs to four classes of functions determined by the following properties: strictly convex versus strictly concave and strictly increasing versus ... see more

Developing further Stein's recent notion of relative end degrees in infinite graphs, we investigate which degree assumptions can force a locally finite graph to contain a given finite minor, or a finite subgraph of given minimum or average degree. This is... see more

This paper considers the degree-diameter problem for undirected circulant graphs. The focus is on extremal graphs of given (small) degree and arbitrary diameter. The published literature only covers graphs of up to degree 7. The approach used to establish... see more

Among bipartite graphs with given order and matching number/vertex cover number/edge cover number/independence number, among multipartite graphs with given order, and among graphs with given order and chromatic number, we present the graphs having the max... see more

Let kKr+1kK_{r+1} be the graph consisting of kk vertex-disjoint copies of the complete graph Kr+1K_{r+1}. Moon [Canad. J. Math. 20 (1968) 95--102] and Simonovits [Theory of Graphs (Proc. colloq., Tihany, 1996)] independently showed that if nn is sufficien... see more

Directed acyclic graphs are often used to model situations and problems in real life. If we consider the topological ordering of the graph as a process of arranging the vertices in the best possible way considering the constraints caused by the direction ... see more

Reduced second Zagreb index has been defined recently. In this paper we characterized extremal bicyclic graphs with pendent vertices with respect to this novel index.

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