Bounding the diameter of a distance-transitive graph
نویسندگان
چکیده
منابع مشابه
The Steiner diameter of a graph
The Steiner distance of a graph, introduced by Chartrand, Oellermann, Tian and Zou in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $Ssubseteq V(G)$, the Steiner distance $d(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. Let $...
متن کاملComplexity of Distance Fraud Attacks in Graph-Based Distance Bounding
Distance bounding (DB) emerged as a countermeasure to the so-called relay attack, which affects several technologies such as RFID, NFC, Bluetooth, and Ad-hoc networks. A prominent family of DB protocols are those based on graphs, which were introduced in 2010 to resist both mafia and distance frauds. The security analysis in terms of distance fraud is performed by considering an adversary that,...
متن کاملBounding the size of a vertex-stabiliser in a finite vertex-transitive graph
In this paper we discuss a method for bounding the size of the stabiliser of a vertex in a G-vertex-transitive graph Γ. In the main result the group G is quasiprimitive or biquasiprimitive on the vertices of Γ, and we obtain a genuine reduction to the case where G is a nonabelian simple group. Using normal quotient techniques developed by the first author, the main theorem applies to general G-...
متن کاملDifferent-Distance Sets in a Graph
A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.The lower and upper different-distance number of a graph are the order of a smallest, respectively largest, maximal different-distance set.We prove that a different-distance set induces either a special type of path or an independent...
متن کاملBounding the Security Number of a Graph
Given a graph G, the security number of G is the cardinality of a minimum secure set of G, the smallest set of vertices S ⊆ V (G) such that for all X ⊆ S, |N [X] ∩ S| ≥ |N [X] − S|. It is believed to be computationally difficult to find the security number of large graphs, so we present techniques for reducing the difficulty of both finding a secure set and determining bounds on the security nu...
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: Journal of Combinatorial Theory, Series B
سال: 1974
ISSN: 0095-8956
DOI: 10.1016/0095-8956(74)90056-2