منابع مشابه
On connected resolvability of graphs
For an ordered set W = {w1, w2, · · · , wk} of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the k-vector r(v|W ) = (d(v, w1), d(v, w2), · · · , d(v, wk)), where d(x, y) represents the distance between the vertices x and y. The set W is a connected resolving set for G if distinct vertices of G have distinct representations with respect to W and the...
متن کامل2-Size Resolvability in Graphs
A vertex u in a graph G resolves a pair of distinct vertices x, y of G if the distance between u and x is different from the distance between u and y. A set W of vertices in G resolves the graph G if every pair of distinct vertices of G is resolved by some vertices in W . The metric dimension of a graph, denoted by dim(G), is the smallest cardinality of a resolving set. A resolving set W for a ...
متن کاملD-resolvability of vertices in planar graphs
It is well known that a vertex of degree 5 in a planar graph is not Dreducible. However, it remains an open question whether all vertices in such a graph areD-resolvable. If so, it would be a stronger result than mere 4-colorability. To investigate the question, we designed and implemented two algorithms, one to 4-color a planar graph and the other to generate internally 6-connected triangulati...
متن کاملConditional resolvability in graphs: a survey
For an ordered setW = {w1,w2, . . . ,wk} of vertices and a vertexv in a connected graphG, the code of v with respect toW is the k-vector cW (v)= (d(v,w1),d(v,w2), . . . ,d(v,wk)), where d(x,y) represents the distance between the vertices x andy . The setW is a resolving set for G if distinct vertices of G have distinct codes with respect to W . The minimum cardinality of a resolving set for G i...
متن کاملSome new connectivity parameters for weighted graphs
In this paper, the concepts of Wiener index of a vertex weighted and edge weighted graphs are discussed. Vertex weight and edge weight of a clique are introduced. Wiener index of a vertex weighted partial cube is also discussed. Also a new concept known as Connectivity index is introduced. A relation between Connectivity index and Wiener index for different graphs are discussed.
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2020
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2019.12.021