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 2

Displaying 21 – 38 of 38

Showing per page

When is the orbit algebra of a group an integral domain ? Proof of a conjecture of P.J. Cameron

Maurice Pouzet (2008)

RAIRO - Theoretical Informatics and Applications

Cameron introduced the orbit algebra of a permutation group and conjectured that this algebra is an integral domain if and only if the group has no finite orbit. We prove that this conjecture holds and in fact that the age algebra of a relational structure R is an integral domain if and only if R is age-inexhaustible. We deduce these results from a combinatorial lemma asserting that if a product of two non-zero elements of a set algebra is zero then there is a finite common tranversal of their...

Wiener and vertex PI indices of the strong product of graphs

K. Pattabiraman, P. Paulraja (2012)

Discussiones Mathematicae Graph Theory

The Wiener index of a connected graph G, denoted by W(G), is defined as ½ ∑ u , v ∈ V ( G ) d G ( u , v ) . Similarly, the hyper-Wiener index of a connected graph G, denoted by WW(G), is defined as ½ W ( G ) + ¼ ∑ u , v ∈ V ( G ) d ² G ( u , v ) . The vertex Padmakar-Ivan (vertex PI) index of a graph G is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. In this paper, the exact formulae for Wiener, hyper-Wiener and vertex PI indices of the strong product G ⊠ K m ₀ , m ₁ , . . . , m r - 1 , where K m ₀ , m ₁ , . . . , m r - 1 is the complete multipartite graph with partite sets of sizes...

Wiener index of generalized stars and their quadratic line graphs

Andrey A. Dobrynin, Leonid S. Mel'nikov (2006)

Discussiones Mathematicae Graph Theory

The Wiener index, W, is the sum of distances between all pairs of vertices in a graph G. The quadratic line graph is defined as L(L(G)), where L(G) is the line graph of G. A generalized star S is a tree consisting of Δ ≥ 3 paths with the unique common endvertex. A relation between the Wiener index of S and of its quadratic graph is presented. It is shown that generalized stars having the property W(S) = W(L(L(S)) exist only for 4 ≤ Δ ≤ 6. Infinite families of generalized stars with this property...

Wiener index of graphs with fixed number of pendant or cut-vertices

Dinesh Pandey, Kamal Lochan Patra (2022)

Czechoslovak Mathematical Journal

The Wiener index of a connected graph is defined as the sum of the distances between all unordered pairs of its vertices. We characterize the graphs which extremize the Wiener index among all graphs on n vertices with k pendant vertices. We also characterize the graph which minimizes the Wiener index over the graphs on n vertices with s cut-vertices.

Wiener index of the tensor product of a path and a cycle

K. Pattabiraman, P. Paulraja (2011)

Discussiones Mathematicae Graph Theory

The Wiener index, denoted by W(G), of a connected graph G is the sum of all pairwise distances of vertices of the graph, that is, W ( G ) = ½ Σ u , v ∈ V ( G ) d ( u , v ) . In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.

Word distance on the discrete Heisenberg group

Sébastien Blachère (2003)

Colloquium Mathematicae

We establish an exact formula for the word distance on the discrete Heisenberg group ℍ₃ with its standard set of generators. This formula is then used to prove the almost connectedness of the spheres for this distance.

Worm Colorings

Wayne Goddard, Kirsti Wash, Honghai Xu (2015)

Discussiones Mathematicae Graph Theory

Given a coloring of the vertices, we say subgraph H is monochromatic if every vertex of H is assigned the same color, and rainbow if no pair of vertices of H are assigned the same color. Given a graph G and a graph F, we define an F-WORM coloring of G as a coloring of the vertices of G without a rainbow or monochromatic subgraph H isomorphic to F. We present some results on this concept especially as regards to the existence, complexity, and optimization within certain graph classes. The focus is...

WORM Colorings of Planar Graphs

J. Czap, S. Jendrol’, J. Valiska (2017)

Discussiones Mathematicae Graph Theory

Given three planar graphs F,H, and G, an (F,H)-WORM coloring of G is a vertex coloring such that no subgraph isomorphic to F is rainbow and no subgraph isomorphic to H is monochromatic. If G has at least one (F,H)-WORM coloring, then W−F,H(G) denotes the minimum number of colors in an (F,H)-WORM coloring of G. We show that (a) W−F,H(G) ≤ 2 if |V (F)| ≥ 3 and H contains a cycle, (b) W−F,H(G) ≤ 3 if |V (F)| ≥ 4 and H is a forest with Δ (H) ≥ 3, (c) W−F,H(G) ≤ 4 if |V (F)| ≥ 5 and H is a forest with...

Currently displaying 21 – 38 of 38

Previous Page 2