Sum graph based access structure in a secret sharing scheme
- Authors: Miller, Mirka , Slamet, Surjadi , Sugeng, Kiki Ariyanti
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Prime Research in Mathematics Vol. 2, no. (2006), p. 113-119
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- Description: Secret sharing scheme is a method to distribute secret information to a set P of participants so that only authorised subsets of P can reconstruct the secret. A set of subsets of P that can reconstruct the secret is called an access structure of the scheme. A simple undirected graph G is called a sum graph if there exists a labeling L of the vertices of G into distinct numbers, usually positive integers, such that any two distinct vertices u and v of G are adjacent if and only if there is a vertex w whose label is L(w) = L(u) + L(v). In this paper, we will show how sum labeling can be used for representing the graphs of the access structures of a secret sharing scheme. We will combine a known secret sharing scheme such as the classical Shamir scheme with a graph access structure represented using sum graph labeling to obtain a new secret sharing scheme.
- Description: C1
- Description: 2003001595
Super edge-antimagic total labeling
- Authors: Sugeng, Kiki Ariyanti , Miller, Mirka , Baca, Martin
- Date: 2006
- Type: Text , Journal article
- Relation: Utilitas Mathematica Vol. 71, no. (2006), p. 131-141
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- Description: A (p, q)-graph G is (a, d)-edge-antimagic total if there exists a bijective function f : V(G) ∪ E(G) → {1,2,...,p + q} such that the edge-weights w(uv) = f(u) + f(v) + f(uv), uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. Moreover, G is said to be super (a, d)-edge-antimagic total if f(V(G)) = {1,2,..., p}. In this paper we study the super (a,d)-edge-antimagic total properties of certain classes of graphs, including ladders, generalized prisms and antiprisrns.
- Description: C1
- Description: 2003001596
Survey of edge antimagic labelings of graphs
- Authors: Miller, Mirka , Baca, Martin , Baskoro, Edy , Ryan, Joe , Simanjuntak, Rinovia , Sugeng, Kiki Ariyanti
- Date: 2006
- Type: Text , Journal article
- Relation: Journal of Indonesian Mathematical Society, MIHMI Vol. 12, no. 1 (2006), p. 113-130
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- Description: C1
- Description: 2003001600
Vertex-magic total labeling of generalized Petersen graphs and convex polytopes
- Authors: Miller, Mirka , Baca, Martin , MacDougall, James
- Date: 2006
- Type: Text , Journal article
- Relation: JCMCC Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 59, no. (2006), p. 89-99
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- Description: To date the study of graph labellings has focused on nding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic labellings for which all graphs admit such a labelling. In particular we consider two types of labellings of the vertices and edges of a graph with distinct positive integers: (1) for every edge the sum of its label and those of its endvertices is some constant (pseudo edge-magic); and (2) for every vertex the sum of its label and those of the edges incident to it is some constant (pseudo vertex-magic). Our aim is to minimise the constant, called the magic number, associated with the labelling. We present lower and upper bounds on the magic number in pseudo edge-magic and pseudo vertex-magic labellings of complete graphs, trees and arbitrary graphs. In a number of cases these bounds are within a constant factor.
- Description: C1
- Description: 2003001602
(a,d)-edge-antimagic total labelings of caterpillars
- Authors: Miller, Mirka , Sugeng, Kiki Ariyanti , Slamin, , Baca, Martin
- Date: 2005
- Type: Text , Journal article
- Relation: Combinatorial Geometry and Graph Theory, LNCS 3330, Lecture Notes in Computer Science, Indonesia-Japan Joint Conference IJCCGGT 2003, Bandung, Indonesia, September 2003, Revised Selected Papers Vol. 3330, no. (2005), p. 169-180
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- Description: For a graph G = (V,E), a bijection g from V (G)∪E(G) into {1, 2, ..., |V (G)|+|E(G)|} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy ∈ E(G), form an arithmetic progression with initial term a and common difference d. An (a, d)-edge-antimagic total labeling g is called super (a, d)-edge-antimagic total if g(V (G)) = {1, 2, ..., |V (G)|}. We study super (a, d)-edge-antimagic total properties of stars Sn and caterpillar Sn1,n2,...,nr .
- Description: C1
- Description: 2003001412
Algebraic insight underpins the use of CAS for modelling
- Authors: Pierce, Robyn
- Date: 2005
- Type: Text , Journal article
- Relation: The Montana Mathematics Enthusiast Vol. 2, no. 2 (2005), p. 107-117
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- Description: Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students developing each of the two key aspects: algebraic expectation and ability to link representations. This framework may be used for both planning teaching and monitoring students’ progress.
- Description: C1
- Description: 2003001447
All (k;g)-cages are k-edge-connected
- Authors: Lin, Yuqing , Miller, Mirka , Rodger, Chris
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Graph Theory Vol. 48, no. 3 (2005), p. 219-227
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- Description: A (k;g)-cage is a k-regular graph with girth g and with the least possible number of vertices. In this paper, we prove that (k;g)-cages are k-edge-connected if g is even. Earlier, Wang, Xu, and Wang proved that (k;g)-cages are k-edge-connected if g is odd. Combining our results, we conclude that the (k;g)-cages are k-edge-connected. © 2005 wiley Periodicals, Inc.
- Description: C1
Complete characterization of almost moore digraphs of degree three
- Authors: Baskoro, Edy , Miller, Mirka , Siran, Jozef , Sutton, Martin
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Graph Theory Vol. 48, no. 2 (2005), p. 112-126
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- Description: It is well known that Moore digraphs do not exist except for trivial cases (degree 1 or diameter 1), but there are digraphs of diameter two and arbitrary degree which miss the Moore bound by one. No examples of such digraphs of diameter at least three are known, although several necessary conditions for their existence have been obtained. In this paper, we prove that digraphs of degree three and diameter k ≥ 3 which miss the Moore bound by one do not exist. © 2004 Wiley Periodicals, Inc.
- Description: C1
- Description: 2003000904
Conjectures and open problems on face antimagic evaluations of graphs
- Authors: Miller, Mirka , Baca, Martin , Baskoro, Edy , Cholily, Yus Mochamad , Jendrol, Stanislav , Lin, Yuqing , Ryan, Joe , Simanjuntak, Rinovia , Slamin, , Sugeng, Kiki Ariyanti
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Indonesian Mathematical Society MIHMI Vol. 11, no. 2 (2005), p. 175-192
- Full Text: false
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- Description: C1
- Description: 2003001408
Exclusive sum labeling of graphs
- Authors: Miller, Mirka , Patel, Deval , Ryan, Joe , Sugeng, Kiki Ariyanti , Slamin, , Tuga, Mauritsius
- Date: 2005
- Type: Text , Journal article
- Relation: The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 137-148
- Full Text: false
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- Description: C1
- Description: 2003001402
Exclusive sum labelings of trees
- Authors: Miller, Mirka , Tuga, Mauritsius , Ryan, Joe , Ryjacek, Zdenek
- Date: 2005
- Type: Text , Journal article
- Relation: The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 109-121
- Full Text: false
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- Description: The notions of
- Description: C1
- Description: 2003001406
Hidden abstract convex functions
- Authors: Rubinov, Alex , Wu, Zhiyou , Li, Duan
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Nonlinear and Convex Analysis Vol. 6, no. 1 (2005), p. 203-216
- Full Text: false
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- Description: C1
- Description: 2003001424
Improved lower bound for the vertex connectivity of (delta;g)-cages
- Authors: Lin, Yuqing , Miller, Mirka , Balbuena, Camino
- Date: 2005
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 299, no. 1-3 (Aug 2005), p. 162-171
- Full Text: false
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- Description: A (delta, g)-cage is a delta-regular graph with girth g and with the least possible number of vertices. We prove that all (delta, g)-cages are r-connected with r >= root(delta + 1) for g >= 7 odd. This result supports the conjecture of Fu, Huang and Rodger that all (delta; g)-cages are delta-connected. (c) 2005 Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003001397
Languages recognized by two-sided automata of graphs
- Authors: Miller, Mirka , Kelarev, Andrei , Sokratova, Olga
- Date: 2005
- Type: Text , Journal article
- Relation: Proceedings of the Estonian Academy of Sciences, Physics Mathematic Vol. 51, no. 1 (2005), p. 46-54
- Full Text: false
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- Description: We introduce two-sided automata defined by directed graphs and describe all languages recognized by these automata.
- Description: C1
- Description: 2003001399
Moore graphs and beyond : A survey of the degree/diameter problem
- Authors: Miller, Mirka , Siran, Jozef
- Date: 2005
- Type: Text , Journal article
- Relation: Electronic Journal of Combinatorics Vol. DS14, no. (2005), p. 1-61
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- Description: The degree/diameter problem is to determine the largest graphs or digraphs of given maximum degree and given diameter. General upper bounds { called Moore bounds { for the order of such graphs and digraphs are attainable only for certain special graphs and digraphs. Finding better (tighter) upper bounds for the maximum possible number of vertices, given the other two parameters, and thus attacking the degree/diameter problem `from above', remains a largely unexplored area. Constructions producing large graphs and digraphs of given degree and diameter represent a way of attacking the degree/diameter problem `from below'. This survey aims to give an overview of the current state-of-the-art of the degree/diameter problem. We focus mainly on the above two streams of research. However, we could not resist mentioning also results on various related problems. These include considering Moore-like bounds for special types of graphs and digraphs, such as vertex-transitive, Cayley, planar, bipartite, and many others, on the one hand, and related properties such as connectivity, regularity, and surface embeddability, on the other hand.
- Description: C1
- Description: 2003001407
Parallel algorithms for generalized clique transversal problems
- Authors: Miller, Mirka , Dahlhaus, Elias , Manuel, Paul
- Date: 2005
- Type: Text , Journal article
- Relation: Australasian Journal of Combinatorics Vol. 33, no. (2005), p. 3-14
- Full Text: false
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- Description: The K ` - clique transversal problem is to locate a minimum collection of cliques of size ` in a graph G such that every maximal clique of size ` in G contains at least one member of the collection. We give an NC algorithm to solve this problem on strongly chordal graphs. Keywords: balanced graphs, strongly chordal graphs, clique transversal, k-fold clique transversal, K ` - clique transversal. 1 Introduction A 0 Gamma 1 matrix is balanced if it does not contain as a submatrix, an edge - vertex incidence matrix of an odd cycle. A 0 Gamma 1 matrix is totally balanced if it does not contain as a submatrix, an edge - vertex incidence matrix of any cycle. A hypergraph H is an ordered pair (V; E) where V is a set of vertices and E is a family of subsets of V . The members of E are called hyperedges of H . Let V = fv 1 ; v 2 ; : : : ; v n g and E = fE 1 ; E 2 ; : : : ; Em g. Let A(H) denote the hyperedge - vertex incidence matrix of a hypergraph H .
- Description: C1
- Description: 2003001400
Relationship between adjacency matrices and super (a,d)-edge-antimagic total labeling of graphs
- Authors: Miller, Mirka , Sugeng, Kiki Ariyanti
- Date: 2005
- Type: Text , Journal article
- Relation: The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 71-82
- Full Text: false
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- Description: C1
- Description: 2003001403
Sigma-porosity in monotonic analysis with applications to optimization
- Authors: Rubinov, Alex
- Date: 2005
- Type: Text , Journal article
- Relation: Abstract and Applied Analysis Vol. 2005, no. 3 (2005), p. 287-305
- Full Text: false
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- Description: We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of strictly conormal sets are $sigma$-porous in corresponding spaces. Some applications to optimization are given.
- Description: C1
- Description: We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of strictly conormal sets are $\sigma$-porous in corresponding spaces. Some applications to optimization are given.
- Description: 2003001421
Sophus Lie's third fundamental theorem and the adjoint functor theorem
- Authors: Hofmann, Karl , Morris, Sidney
- Date: 2005
- Type: Text , Journal article
- Relation: Journal of Group Theory Vol. 8, no. 1 (2005), p. 115-133
- Full Text: false
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- Description: The essential attributes of a Lie group G are the associated Lie algebra LðGÞ and the exponential function exp : LðGÞ ! G. The prescription L operates not only on Lie groups but also on morphisms between them: it is a functor. Many features of Lie theory are shared by classes of topological groups which are much larger than that of Lie groups; these classes include the classes of compact groups, locally compact groups, and pro-Lie groups, that is, complete topological groups having arbitrarily small normal subgroups N such that G=N is a (finitedimensional) Lie group. Considering the functor L it is therefore appropriate to contemplate more general classes of topological groups. Certain functorial properties of the assignment of a Lie algebra to a topological group (where possible) will be essential. What is new here is that we will introduce a functorial assignment from Lie algebras to groups and investigate to what extent it is inverse to the Lie algebra functor L. While the Lie algebra functor is well known and is cited regularly, the existence of a Lie group functor available to be cited and applied appears less well known. Sophus Lie’s Third Fundamental Theorem says that for each finite-dimensional real Lie algebra there is a Lie group whose Lie algebra is (isomorphic to) the given one; but even in classical circumstances it is not commonly known that this happens in a functorial fashion and what the precise relationship between the Lie algebra functor and the Lie group functor is.
- Description: C1
- Description: 2003001415
Super (a,d)-vertex-antimagic total labelings
- Authors: Miller, Mirka , Sugeng, Kiki Ariyanti , Lin, Yuqing , Baca, Martin
- Date: 2005
- Type: Text , Journal article
- Relation: The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 91-102
- Full Text: false
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- Description: C1
- Description: 2003001401