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and the fault tolerant hamiltonicity of the alternating group graphs . In this article, we propose a new concept called panpositionable hamiltonicity. A hamiltonian graph G is panpositionable if for any two ...
representation of a graph is a collection of k-bend paths such that each path in the collection represents a vertex of the graph and two such paths intersect if and only if the vertices they represent are adjacent ...
by the shortest path from the source to $v$ among the so called {\em$ t+$light paths }. A directed path between two vertices is $t+$light if it contains at most $t$ more edges than the minimum edge-cardinality ...
LetG = (V, E) be a finite graph . The setL of labeled vertices is initially empty. Two players A and B move alternately (A first), by choosing an unlabled vertexu ε ∈V\L; thenu itself and all vertices ...
Abstract: Let $d(x,y)$ denote the length of a shortest path between vertices $x$ and $y$ in a graph $G$ with vertex set $V$. For a positive integer $k$, let $d_k(x,y)=\min\{d(x,y), k+1\}$ and $R_k\{x ...
a resistance of $$1 \varOmega $$ 1 Ω , the equivalent resistance of the graph between each pair of vertices may be used as a distance. Based upon random walks in graphs , Stephenson and Zelen (Soc Netw 11 ...
of simple connected undirected graphs whenever their order n tends to +∞ we have (7) Thus, for , we immediately obtain Definition 1. The path graph Pm, m ≥ 2, is a simple connected undirected graph with two ...
-24$| |$8n-20$| 9 A |$4$|-cycle |$8n-24$| |$8n-20$| Remark: |$K_{1,3}+e$| is a graph that adds an edge between two vertices of degree one in |$K_{1,3}$|. Open in new tab Table 2. All cases for |$U=\{u ...
one for the basic case of single-edge paths . Some preliminary results on the paths between vertices in a tree were given by Roverato & Castelo (2018). In this article, we consider concentration graph ...
probabilistic and worst-case properties of profiles. We restrict our attention to trees. Trees are a natural first case to consider as there is exactly one shortest path between any two vertices . We consider ...
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