• Title/Summary/Keyword: finite graph

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FINITE GROUPS WHOSE INTERSECTION GRAPHS ARE PLANAR

  • Kayacan, Selcuk;Yaraneri, Ergun
    • Journal of the Korean Mathematical Society
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    • v.52 no.1
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    • pp.81-96
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    • 2015
  • The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if $H{\cap}K{\neq}1$ where 1 denotes the trivial subgroup of G. In this paper we characterize all finite groups whose intersection graphs are planar. Our methods are elementary. Among the graphs similar to the intersection graphs, we may count the subgroup lattice and the subgroup graph of a group, each of whose planarity was already considered before in [2, 10, 11, 12].

LONG PATHS IN THE DISTANCE GRAPH OVER LARGE SUBSETS OF VECTOR SPACES OVER FINITE FIELDS

  • BENNETT, MICHAEL;CHAPMAN, JEREMY;COVERT, DAVID;HART, DERRICK;IOSEVICH, ALEX;PAKIANATHAN, JONATHAN
    • Journal of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.115-126
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    • 2016
  • Let $E{\subset}{\mathbb{F}}^d_q$, the d-dimensional vector space over the finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x, y 2 E by an edge if ${\parallel}x-y{\parallel}:=(x_1-y_1)^2+{\cdots}+(x_d-y_d)^2=1$. We shall prove that the non-overlapping chains of length k, with k in an appropriate range, are uniformly distributed in the sense that the number of these chains equals the statistically correct number, $1{\cdot}{\mid}E{\mid}^{k+1}q^{-k}$ plus a much smaller remainder.

SPANNING 3-FORESTS IN BRIDGES OF A TIGHT SEMIRING IN AN LV-GRAPH

  • Jung, Hwan-Ok
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1307-1318
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    • 2009
  • An infinite locally finite plane graph is an LV-graph if it is 3-connected and VAP-free. In this paper, as a preparatory work for solving the problem concerning the existence of a spanning 3-tree in an LV-graph, we investigate the existence of a spanning 3-forest in a bridge of type 0,1 or 2 of a tight semi ring in an LV-graph satisfying certain conditions.

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5-CYCLABILITY IN INFINITE PLANAR GRAPHS

  • JUNG HWAN-OK
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.537-543
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    • 2005
  • A graph is k-cyclable if given k vertices there is a cycle that contains the k vertices. Sallee showed that every finite 3-connected planar graph is 5-cyclable. In this paper Sallee's result is extended to 3-connected infinite locally finite VAP-free plane graphs containing no unbounded faces.

RESIDUAL FINITENESS AND ABELIAN SUBGROUP SEPARABILITY OF SOME HIGH DIMENSIONAL GRAPH MANIFOLDS

  • Kim, Raeyong
    • Korean Journal of Mathematics
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    • v.29 no.3
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    • pp.603-612
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    • 2021
  • We generalize 3-manifolds supporting non-positively curved metric to construct manifolds which have the following properties : (1) They are not locally CAT(0). (2) Their fundamental groups are residually finite. (3) They have subgroup separability for some abelian subgroups.

A NEW CHARACTERIZATION OF $A_p$ WHERE p AND p-2 ARE PRIMES

  • Iranmanesh, A.;Alavi, S.H.
    • Journal of applied mathematics & informatics
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    • v.8 no.3
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    • pp.889-897
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    • 2001
  • Based on the prime graph of a finite simple group, its order is the product of its order components (see[4]). It is known that Suzuki-Ree groups [6], $PSL_2(q)$ [8] and $E_8(q)$ [7] are uniquely deternubed by their order components. In this paper we prove that the simple groups $A_p$ are also unipuely determined by their order components, where p and p-2 are primes.

AN EXTENSION OF SALLEE'S THEOREM TO INFINITE LOCALLY FINITE VAP-FREE PLANE GRAPHS

  • Jung Hwan-Ok
    • Journal of applied mathematics & informatics
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    • v.22 no.1_2
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    • pp.83-93
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    • 2006
  • A graph is k-cyclable if given k vertices there is a cycle that contains the k vertices. Sallee showed that every finite 3-connected planar graph is 5-cyclable. In this paper, by characterizing the circuit graphs and investigating the structure of LV-graphs, we extend his result to 3-connected infinite locally finite VAP-free plane graphs.

EMBEDDING DISTANCE GRAPHS IN FINITE FIELD VECTOR SPACES

  • Iosevich, Alex;Parshall, Hans
    • Journal of the Korean Mathematical Society
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    • v.56 no.6
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    • pp.1515-1528
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    • 2019
  • We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A{\subseteq}F^d_q$ and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions $d{\geq}2t$.

VOLUME OF GRAPH POLYTOPES FOR THE PATH-STAR TYPE GRAPHS

  • Ju, Hyeong-Kwan;Seo, Soo-Jeong
    • Honam Mathematical Journal
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    • v.38 no.1
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    • pp.71-84
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    • 2016
  • The aim of this work is to compute the volume of the graph polytope associated with various type of finite simple graphs composed of paths and stars. Recurrence relations are obtained using the recursive volume formula (RVF) which was introduced in Lee and Ju ([3]). We also discussed the relationship between the volume of the graph polytopes and the number of linear extensions of the associated posets for given bipartite graphs.