منابع مشابه
2-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 کاملOn 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 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 کاملWeak signed Roman k-domination in graphs
Let $kge 1$ be an integer, and let $G$ be a finite and simple graph with vertex set $V(G)$.A weak signed Roman $k$-dominating function (WSRkDF) on a graph $G$ is a function$f:V(G)rightarrow{-1,1,2}$ satisfying the conditions that $sum_{xin N[v]}f(x)ge k$ for eachvertex $vin V(G)$, where $N[v]$ is the closed neighborhood of $v$. The weight of a WSRkDF $f$ is$w(f)=sum_{vin V(G)}f(v)$. The weak si...
متن کاملWeak signed Roman domination in graphs
A {em weak signed Roman dominating function} (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as afunction $f:V(G)rightarrow{-1,1,2}$ having the property that $sum_{xin N[v]}f(x)ge 1$ for each $vin V(G)$, where $N[v]$ is theclosed neighborhood of $v$. The weight of a WSRDF is the sum of its function values over all vertices.The weak signed Roman domination number of $G...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2016
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1853