All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 399

Showing per page

Sharp Upper Bounds for Generalized Edge-Connectivity of Product Graphs

Yuefang Sun (2016)

Discussiones Mathematicae Graph Theory

The generalized k-connectivity κk(G) of a graph G was introduced by Hager in 1985. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized k-edge-connectivity which is defined as λk(G) = min{λ(S) : S ⊆ V (G) and |S| = k}, where λ(S) denote the maximum number ℓ of pairwise edge-disjoint trees T1, T2, . . . , Tℓ in G such that S ⊆ V (Ti) for 1 ≤ i ≤ ℓ. In this paper, we study the generalized edge- connectivity of product graphs and obtain sharp upper bounds...

Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs

Weige Xi, Ligong Wang (2016)

Discussiones Mathematicae Graph Theory

Let G = (V (G),E(G)) be a simple strongly connected digraph and q(G) be the signless Laplacian spectral radius of G. For any vertex vi ∈ V (G), let d+i denote the outdegree of vi, m+i denote the average 2-outdegree of vi, and N+i denote the set of out-neighbors of vi. In this paper, we prove that: (1) (1) q(G) = d+1 +d+2 , (d+1 ≠ d+2) if and only if G is a star digraph [...] ,where d+1, d+2 are the maximum and the second maximum outdegree, respectively [...] is the digraph on n vertices obtained...

Short cycles of low weight in normal plane maps with minimum degree 5

Oleg V. Borodin, Douglas R. Woodall (1998)

Discussiones Mathematicae Graph Theory

In this note, precise upper bounds are determined for the minimum degree-sum of the vertices of a 4-cycle and a 5-cycle in a plane triangulation with minimum degree 5: w(C₄) ≤ 25 and w(C₅) ≤ 30. These hold because a normal plane map with minimum degree 5 must contain a 4-star with w ( K 1 , 4 ) ≤ 30 . These results answer a question posed by Kotzig in 1979 and recent questions of Jendrol’ and Madaras.

Short paths in 3-uniform quasi-random hypergraphs

Joanna Polcyn (2004)

Discussiones Mathematicae Graph Theory

Frankl and Rödl [3] proved a strong regularity lemma for 3-uniform hypergraphs, based on the concept of δ-regularity with respect to an underlying 3-partite graph. In applications of that lemma it is often important to be able to "glue" together separate pieces of the desired subhypergraph. With this goal in mind, in this paper it is proved that every pair of typical edges of the underlying graph can be connected by a hyperpath of length at most seven. The typicality of edges is defined in terms...

Sierpiński graphs as spanning subgraphs of Hanoi graphs

Andreas Hinz, Sandi Klavžar, Sara Zemljič (2013)

Open Mathematics

Hanoi graphs H pn model the Tower of Hanoi game with p pegs and n discs. Sierpinski graphs S pn arose in investigations of universal topological spaces and have meanwhile been studied extensively. It is proved that S pn embeds as a spanning subgraph into H pn if and only if p is odd or, trivially, if n = 1.

Sign patterns that allow eventual positivity.

Berman, Abraham, Catral, Minerva, Dealba, Luz Maria, Elhashash, Abed, Hall, Frank J., Hogben, Leslie, Kim, In-Jae, Olesky, Dale D., Tarazaga, Pablo, Tsatsomeros, Michael J., van den Driessche, Pauline (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Signed 2-domination in caterpillars

Bohdan Zelinka (2004)

Mathematica Bohemica

A caterpillar is a tree with the property that after deleting all its vertices of degree 1 a simple path is obtained. The signed 2-domination number γ s 2 ( G ) and the signed total 2-domination number γ st 2 ( G ) of a graph G are variants of the signed domination number γ s ( G ) and the signed total domination number γ st ( G ) . Their values for caterpillars are studied.

Currently displaying 61 – 80 of 399