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 کاملAlmost Self-centered Median and Chordal Graphs
Almost self-centered graphs were recently introduced as the graphs with exactly two non-central vertices. In this paper we characterize almost selfcentered graphs among median graphs and among chordal graphs. In the first case P4 and the graphs obtained from hypercubes by attaching to them a single leaf are the only such graphs. Among chordal graph the variety of almost self-centered graph is m...
متن کاملA Generalized Distance in Graphs and Centered Partitions
This paper is concerned with a new distance in undirected graphs with weighted edges, which gives new insights into the structure of all minimum spanning trees of a graph. This distance is a generalized one, in the sense that it takes values in a certain Heyting semigroup. More precisely, it associates with each pair of distinct vertices in a connected component of a graph the set of all paths ...
متن کاملSome Notes on Minimal Self–Centered Graphs
A graph is called self–centered if all of its vertices have the same eccentricity. We prove some new properties of such graphs and obtain all minimal self–centered graphs of up to 10 vertices.
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ژورنال
عنوان ژورنال: Journal of Mathematics and Computer Science
سال: 2014
ISSN: 2008-949X
DOI: 10.22436/jmcs.010.04.02