• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.971-995
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• 2014

The parts of semi-rigid connected and partially embedded piles in elastic soil, above the soil and embedded in the soil are called the first region and second region, respectively. The upper end of the pile in the first region is supported by linear-elastic rotational spring. The forth order differential equations of both region for critical buckling load of partially embedded and semi-rigid connected pile with shear deformation are established using small-displacement theory and Winkler hypothesis. These differential equations are solved by differential transform method (DTM) and analytical method and critical buckling loads of semirigid connected and partially embedded pile are obtained, results are given in tables and graphs are presented for investigating the effects of relative stiffness of the pile and flexibility of rotational spring.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.221-225
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• 2016

For a connected graph G = (V, E), its inverse degree is defined as $\sum_{{\upsilon}{\in}{V}}^{}\frac{1}{d(\upsilon)}$. Using an upper bound for the inverse degree of a graph obtained by Cioabă in [4], we in this note present sufficient conditions for some Hamiltonian properties and k-connectivity of a graph.

• Proceedings of the IEEK Conference
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• 2002.06c
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• pp.63-66
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• 2002

In this paper, we consider the hamiltonian properties of m ${\times}$ n mesh networks with two wrap-around edges. We describe sufficient condition that at least two edges should be added to a mesh to make it hamiltonian-connected. We propose two graphs, M1(ｍ,n) and M2(ｍ,n). These are obtained by adding one and two edges respectively in the ｍ${\times}$ｎ mesh. We show the hamiltonian properties of M1(ｍ,n) and prove that M2(m, n) is hamiltonian-connected using the hamiltonian properties of M1(ｍ,n).

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.763-787
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• 2017

A graph is called 1-planar if it can be drawn in the Euclidean plane ${\mathbb{R}}^2$ such that each edge is crossed by at most one other edge. The weight of an edge is the sum of degrees of two ends. It is known that every planar graph of minimum degree ${\delta}{\geq}3$ has an edge with weight at most 13. In the present paper, we show the existence of edges with weight at most 25 in 3-connected 1-planar graphs.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.7-14
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• 2001

Let G be a connected graph. A pebbling move on a graph G is taking two pebbles off one vertex and placing one of them on an adjacent vertex. The pebbling number of a connected graph G, f(G), is the least n such that any distribution of n pebbles on the vertices of G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. In this paper, the pebbling numbers of the lexicographic products of some graphs are computed.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.341-354
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• 2016

In this paper, the exact formulae for the generalized product degree distance, reciprocal product degree distance and product degree distance of tensor product of a connected graph and the complete multipartite graph with partite sets of sizes m₀, m₁, ⋯ , m_r−1 are obtained.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.851-860
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• 2008

A countable locally finite triangulation is a strong triangulation if a representation of the graph contains no vertex- or edge-accumulation points. In this paper we exhibit the structure of an infinite strong triangulation and prove the existence of connected spanning subgraph with maximum degree 4 in such a graph

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.1
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• pp.63-73
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• 1988

In this paper, an algorithm is proposed to evaluate the source-to-terminal reliability, the probability that a source node can communicate with a terminal node, in a probabilistic derected graph. By using Satyanaratana's factoring $theorem^{(7)}$, the original graph can be partitioned into two reduced graphs obtained by contracting and deleting the edge connected to the source node in the probabilistic directed graph. The edge removal proposed in this paper and the general series-parallel reduction can then be applied to the reduced graph. This edge reduction can be applied recursively to the reduced graphs until a source node can be connected to a terminal node by one edge. A computer program which can be applied to evaluating the source-to-terminal reliability in a complex and large network has also been developed.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.349-355
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• 2016

For any integer $n{\geq}2$, each palindrome of n induces a circulant graph of order n. It is known that for each integer $n{\geq}2$, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes ${\sigma}$ with $gcd({\sigma})=1$ to the connected circulant graphs. It was also shown that the number of palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ is the same number of aperiodic palindromes of n. Let $a_n$ (resp. $b_n$) be the number of aperiodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). Let $c_n$ (resp. $d_n$) be the number of periodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). In this paper, we calculate the numbers $a_n$, $b_n$, $c_n$, $d_n$ in two ways. In Theorem 2.3, we $n_d$ recurrence relations for $a_n$, $b_n$, $c_n$, $d_n$ in terms of $a_d$ for $d{\mid}n$ and $d{\neq}n$. Afterwards, we nd formulae for $a_n$, $b_n$, $c_n$, $d_n$ explicitly in Theorem 2.5.

• The KIPS Transactions:PartB
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• v.13B no.2 s.105
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• pp.149-154
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• 2006

The main purpose of document summarization is to reduce the complexity of documents that are consisted of sub-themes. Also it is to create summarization which includes the sub-themes. This paper proposes a summarization system which could extract any salient sentences in accordance with sub-themes by using graph division. A document can be represented in graphs by using chosen representative terms through term relativity analysis based on co-occurrence information. This graph, then, is subdivided to represent sub-themes through connected information. The divided graphs are types of sentence clustering which shows a close relationship. When salient sentences are extracted from the divided graphs, summarization consisted of core elements of sentences from the sub-themes can be produced. As a result, the summarization quality will be improved.