منابع مشابه
On edge detour graphs
For two vertices u and v in a graph G = (V, E), the detour distance D(u, v) is the length of a longest u–v path in G. A u–v path of length D(u, v) is called a u–v detour. A set S ⊆ V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn1(G) of G is the minimum order of its edge detour sets and any edge detour set of order dn1...
متن کاملNontraceable detour graphs
The detour order (of a vertex v) of a graph G is the order of a longest path (beginning at v). The detour sequence of G is a sequence consisting of the detour orders of its vertices. A graph is called a detour graph if its detour sequence is constant. The detour deficiency of a graph G is the difference between the order of G and its detour order. Homogeneously traceable graphs are therefore de...
متن کاملDetour Chromatic Numbers
The nth detour chromatic number, χn(G) of a graph G is the minimum number of colours required to colour the vertices of G such that no path with more than n vertices is monocoloured. The number of vertices in a longest path of G is denoted by τ (G) . We conjecture that χn(G) ≤ d τ(G) n e for every graph G and every n ≥ 1 and we prove results that support the conjecture. We also present some suf...
متن کاملBRST Detour Quantization
We present the BRST cohomologies of a class of constraint (super) Lie algebras as detour complexes. By giving physical interpretations to the components of detour complexes as gauge invariances, Bianchi identities and equations of motion we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. A...
متن کاملOn Detour Index
The detour index of a connected graph is defined as the sum of the detour distances (lengths of longest paths) between unordered pairs of vertices of the graph. We give bounds for the detour index, determine the graphs with minimum and maximum detour indices respectively in the class of n-vertex unicyclic graphs with cycle length r, where 3 ≤ r ≤ n−2, and the graphs with the first, the second a...
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ژورنال
عنوان ژورنال: CAUCHY
سال: 2011
ISSN: 2086-0382
DOI: 10.18860/ca.v2i1.1802