The search session has expired. Please query the service again.
Displaying 361 –
376 of
376
The concept of an object-system is a common generalization of simple graph, digraph and hypergraph. In the theory of generalised colourings of graphs, the Unique Factorization Theorem (UFT) for additive induced-hereditary properties of graphs provides an analogy of the well-known Fundamental Theorem of Arithmetics. The purpose of this paper is to present UFT for object-systems. This result generalises known UFT for additive induced-hereditary and hereditary properties of graphs and digraphs. Formal...
Let ₁, ₂ be graph properties. A vertex (₁,₂)-partition of a graph G is a partition V₁,V₂ of V(G) such that for i = 1,2 the induced subgraph has the property . A property ℜ = ₁∘₂ is defined to be the set of all graphs having a vertex (₁,₂)-partition. A graph G ∈ ₁∘₂ is said to be uniquely (₁,₂)-partitionable if G has exactly one vertex (₁,₂)-partition. In this note, we show the existence of uniquely partitionable planar graphs with respect to hereditary additive properties having a forbidden tree....
The AutoGraphiX 2 system is used to compare the index of a connected graph G with a number of other graph theoretical invariants, i.e., chromatic number, maximum, minimum and average degree, diameter, radius, average distance, independence and domination numbers. In each case, best possible lower and upper bounds, in terms of the order of G, are sought for sums, differences, ratios and products of the index and another invariant. There are 72 cases altogether: in 7 cases known results were reproduced,...
Given a 2-connected graph G on n vertices, let G* be its partially square graph, obtained by adding edges uv whenever the vertices u,v have a common neighbor x satisfying the condition , where . In particular, this condition is satisfied if x does not center a claw (an induced ). Clearly G ⊆ G* ⊆ G², where G² is the square of G. For any independent triple X = x,y,z we define
σ̅(X) = d(x) + d(y) + d(z) - |N(x) ∩ N(y) ∩ N(z)|.
Flandrin et al. proved that a 2-connected graph G is hamiltonian if...
Let be a finite lattice with a least element 0. is an annihilating-ideal graph of in which the vertex set is the set of all nontrivial ideals of , and two distinct vertices and are adjacent if and only if . We completely characterize all finite lattices whose line graph associated to an annihilating-ideal graph, denoted by , is a planar or projective graph.
Currently displaying 361 –
376 of
376