[PDF] Top 20 On graphs with representation number 3

... Comparability graphs correspond to partially ordered sets (posets), and the question whether such a graph can be permutationally k-represented is equivalent to the question whether the respective poset can be ... See full document

... representation number is dn/2e. This result not only provides a com- plete solution to the open Problem 7.4.2 in [8], but also gives a nega- tive answer to the question raised in Problem 7.2.7 in [8] on ... See full document

... Example 1. Consider a thorn(y) complete graph K n ? , n ≥ 3 with the vertices of K n labelled v 1 , v 2 , v 3 , . . . , v n . Without loss of generality assume that t i ≥ 1 pendant vertices (thorns) are ... See full document

... domination number and the irredundance number of a graph G, ...< 3 ir(T ...≤ 3 ir(G) for any block graph G and for any graph G with cyclomatic number µ(G) ≤ ... See full document

... process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for ... See full document

... The concept of Steiner domination number of a graph was introduced by J.John,G.Edwin and P. PaulSudhahar [3]. For a connected graph G, a set of vertices W inG is called a Steiner dominating set if W is both ... See full document

... unique graphs with geometric numbers 6, 8 and ...geometric number is 7. There exist graphs whose greatest geometric number is 3p or the first geometric number is ...geometric ... See full document

... Let G V, E be a graph with vertex set V and edge set E. For a vertex v ∈ V, the open neighbourhood of v in G is Nv {u ∈ V | uv ∈ E}, and Nv Nv ∪ {v} is its closed neighbourhood. For a graph G, and a subset S ⊆ V , we let ... See full document

... minimum number of monochromatic triangles in a complete graph whose edge set is ...complete graphs whose edge sets are coloured with more than two ...minimum number of monochromatic triangles in a ... See full document

... minimum 3-dominating set of BF(5). If possible let there be a 3-dominating set S such that ...domination number of BF(n) is even, due to the symmetry of the graph, │S│ is ...domination number ... See full document

... In the area of mixed domination several new concepts have been appeared. The concept of a vertex which m-dominates an edge and the concept of an edge which m-dominates a vertex have been defined and studied by some ... See full document

... Halin graphs as a class of minimally 3-vertex-connected graphs: for every edge in the graph, the removal of that edge reduces the connectivity of the ...These graphs gained in significance ... See full document

... The notion of Asteroidal triples was introduced by Lekkerkerker and Boland [6]. D.G.Corneil and others [2], Ekkehard Kohler [3] further investigated asteroidal triples. Walter generalized the concept of asteroidal ... See full document

... fullerene graphs are considered by many mathematicians in all over the ...fullerene graphs were defined as 3regular planar 3connected graphs whose faces are pentagons and ... See full document

... An interesting variant of domination problem is to ask how many dominating sets one can pack into a given graph G and the main question is how to partition the vertex set of a graph into maximum number of disjoint ... See full document

... Abstract-- Let G be a connected graph of order n ≥ 3 and let k-labeling c: E(G) → {1, 2, 3, . . . ,k } of the edges of G, (where adjacent edges may be colored the same). For each vertex v of G, the color ... See full document

... Abstract. In a graph G , a spanning tree T is said to be a tree t-spanner of the graph G if the distance between any two vertices in T is at most t times their distance in G . The tree t-spanner has many applications in ... See full document

... total number of colours requiered for the proper colouring of the graph G is called the chromatic number of that ...chromatic number of the above graph is ... See full document

... the number of vertices in the graph in question, by a number of ...follows. Number the vertices from 1 to n, and represent a word w that we are looking for by kn integer variables A i,j , ... See full document

... Lemma 4 and the results given in Section 5 can be used to find the number of kdecompositions of non-basic graphs with cyclomatic number 3... gether with Theorem 9, can be used to find th[r] ... See full document