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Radius, Diameter, and Minimum Degree
, 1989
"... We give asymptotically sharp upper bounds for the maximum diameter and radius of (i) a connected graph, {ii) a connected trianglefree graph, (iii) a connected C,free graph with n vertices and with minimum degree 6, where n tends to infinity. Some conjectures for J&free graphs are also stated. ..."
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We give asymptotically sharp upper bounds for the maximum diameter and radius of (i) a connected graph, {ii) a connected trianglefree graph, (iii) a connected C,free graph with n vertices and with minimum degree 6, where n tends to infinity. Some conjectures for J&free graphs are also stated.
TMME,Vol.1, no.1,p.9 Radius, Diameter, Circumference, π, Geometer’s Sketchpad©, and You!
"... I truly believe learning mathematics can be a fun experience for children of all ages. It is up to us, the teachers, to present math as an interesting application. The addition of computers into our everchanging world has given us an important tool, which can assist us on our journey to teach math ..."
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I truly believe learning mathematics can be a fun experience for children of all ages. It is up to us, the teachers, to present math as an interesting application. The addition of computers into our everchanging world has given us an important tool, which can assist us on our journey to teach math in new fun and interesting ways. The Program Geometer’s Sketchpad © is one of
Unreliable Sensor Grids: Coverage, Connectivity and Diameter
 In Proceedings of IEEE INFOCOM
, 2003
"... We consider an unreliable wireless sensor gridnetwork with n nodes placed in a square of unit area. We are interested in the coverage of the region and the connectivity of the network. We first show that the necessary and sufficient conditions for the random grid network to cover the unit square reg ..."
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Cited by 216 (9 self)
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region as well as ensure that the active nodes are connected are of the form p(n)r ,wherer(n) is the transmission radius of each node and p(n) is the probability that a node is "active" (not failed). This result indicates that, when n is large, even if each node is highly unreliable
ON CYCLES IN GRAPHS WITH SPECIFIED RADIUS AND DIAMETER
"... Abstract. Let G be a graph of radius r and diameter d with d ≤ 2r − 2. We show that G contains a cycle of length at least 4r−2d, i.e. for its circumference it holds c(G) ≥ 4r−2d. Moreover, for all positive integers r and d with r ≤ d ≤ 2r − 2 there exists a graph of radius r and diameter d with cir ..."
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Abstract. Let G be a graph of radius r and diameter d with d ≤ 2r − 2. We show that G contains a cycle of length at least 4r−2d, i.e. for its circumference it holds c(G) ≥ 4r−2d. Moreover, for all positive integers r and d with r ≤ d ≤ 2r − 2 there exists a graph of radius r and diameter d
On the Diameter and Radius of Random Subgraphs of the Cube
"... Abstract. The ndimensional cube Q n is the graph whose vertices are the subsets of {1,..., n}, with two vertices adjacent if and only if their symmetric difference is a singleton. Clearly Q n has diameter and radius n. Write M = n2 n−1 = e(Q n) for the size of Q n. Let ˜Q = (Qt) M 0 random Q nproc ..."
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Abstract. The ndimensional cube Q n is the graph whose vertices are the subsets of {1,..., n}, with two vertices adjacent if and only if their symmetric difference is a singleton. Clearly Q n has diameter and radius n. Write M = n2 n−1 = e(Q n) for the size of Q n. Let ˜Q = (Qt) M 0 random Q n
Carrying Location Objects in RADIUS and Diameter
, 2009
"... This document describes procedures for conveying accessnetwork ownership and location information based on civic and geospatial location formats in Remote Authentication DialIn User Service (RADIUS) and Diameter. The distribution of location information is a privacysensitive task. Dealing with me ..."
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This document describes procedures for conveying accessnetwork ownership and location information based on civic and geospatial location formats in Remote Authentication DialIn User Service (RADIUS) and Diameter. The distribution of location information is a privacysensitive task. Dealing
Generalised Eccentricity, Radius and Diameter in Graphs
"... For a vertex v and a (k−1)element subset P of vertices of a graph, one can define the distance from v to P in various ways, including the minimum, average, and maximum distance from v to P. Associated with each of these distances, one can define the keccentricity of the vertex v as the maximum dist ..."
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distance over all P, and the keccentricity of the set P as the maximum distance over all v. If k = 2 one is back with the normal eccentricity. We study here the properties of these eccentricity measures, especially bounds on the associated radius (minimum keccentricity) and diameter (maximum k
Results 1  10
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226,131