• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2009년도 세계 도시지반공학 심포지엄
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• pp.1141-1146
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• 2009

The compressibility of clay has been expressed e-log p' graph. In natural clay, e-log p' graph are changed by deposition condition and chemical cementation as well as Atterberg limits, whereas in reconstituted clay, it is generally known that e-log p’ curve is varied with Atterberg limits. However, e-log p' graph is possible to change according to the reconstituting methods and test conditions. In this study, consolidation tests are performed as various test condition for reconstituted Busan clay. Test results show that the relationship e/$e_L$ and log p' is almost constant with $e_L$. And the compression index obtained from slurry method sample is larger than one obtained from kneading method sample. Intrinsic compression line (ICL) of Busan clay is identical with ICL suggested by Burland.

• 대한수학회보
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• 제54권2호
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• pp.507-519
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• 2017

We present an upper bound on the Cheeger constant of a distance-regular graph. Recently, the authors found an upper bound on the Cheeger constant of distance-regular graph under a certain restriction in their previous work. Our new bound in the current paper is much better than the previous bound, and it is a general bound with no restriction. We point out that our bound is explicitly computable by using the valencies and the intersection matrix of a distance-regular graph. As a major tool, we use the discrete Green's function, which is defined as the inverse of ${\beta}$-Laplacian for some positive real number ${\beta}$. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.77-83
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• 2024

Chung defined a pebbling move on a graph G as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The monophonic pebbling number guarantees that a pebble can be shifted in the chordless and the longest path possible if there are any hurdles in the process of the supply chain. For a connected graph G a monophonic path between any two vertices x and y contains no chords. The monophonic pebbling number, µ(G), is the least positive integer n such that for any distribution of µ(G) pebbles it is possible to move on G allowing one pebble to be carried to any specified but arbitrary vertex using monophonic a path by a sequence of pebbling operations. The aim of this study is to find out the monophonic pebbling numbers of the sun graphs, (C_n × P₂) + K₁ graph, the spherical graph, the anti-prism graphs, and an n-crossed prism graph.

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.83-93
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• 2017

The Cayley graph ${\Gamma}=Cay(G,S)$ is called normal edge-transitive if $N_A(R(G))$ acts transitively on the set of edges of ${\Gamma}$, where $A=Aut({\Gamma})$ and R(G) is the regular subgroup of A. In this paper, we determine all hexavalent normal edge-transitive Cayley graphs on groups of order pqr, where p > q > r > 2 are prime numbers.

• Journal of Applied and Pure Mathematics
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• 제6권3_4호
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• pp.127-139
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• 2024

Let G be a (p, q) graph. Pair difference cordial number of a graph G is the least positive integer m such that G∪mK₂ is pair difference cordial. It is denoted by PDC_𝜂(G). In this paper we find the pair difference cordial number of bistar, complete, helm, star, wheel.

• Earthquakes and Structures
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• 제10권1호
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• pp.25-51
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• 2016

In this study, graph product rules are applied to the dynamic analysis of regular skeletal structures. Graph product rules have recently been utilized in structural mechanics as a powerful tool for eigensolution of symmetric and regular skeletal structures. A structure is called regular if its model is a graph product. In the first part of this paper, the formulation of time history dynamic analysis of regular structures under seismic excitation is derived using graph product rules. This formulation can generally be utilized for efficient linear elastic dynamic analysis using vibration modes. The second part comprises of random vibration analysis of regular skeletal structures via canonical forms and closed-form eigensolution of matrices containing special patterns for symmetric structures. In this part, the formulations are developed for dynamic analysis of structures subjected to random seismic excitation in frequency domain. In all the proposed methods, eigensolution of the problems is achieved with less computational effort due to incorporating graph product rules and canonical forms for symmetric and cyclically symmetric structures.

• 대한수학회논문집
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• 제22권2호
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• pp.277-287
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• 2007

We prove that if a graph G of bounded degree has finitely many p-hyperbolic ends($1) in which every bounded energy finite p-harmonic function is asymptotically constant for almost every path, then the set $\mathcal{HBD}_p(G)$ of all bounded energy finite p-harmonic functions on G is in one to one corresponding to $\mathbf{R}^l$, where $l$ is the number of p-hyperbolic ends of G. Furthermore, we prove that if a graph G' is roughly isometric to G, then $\mathcal{HBD}_p(G')$ is also in an one to one correspondence with $\mathbf{R}^l$.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.387-401
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• 2001

If the distance between two vertices becomes longer after the removal of a vertex u, then u is called a hinge vertex. In this paper, a linear time sequential algorithm is presented to find all hinge vertices of an interval graph. Also, a parallel algorithm is presented which takes O(n/P + log n) time using P processors on an EREW PRAM.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.577-580
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• 2021

For a finite simplicial graph 𝚪, let G(𝚪) denote the right-angled Artin group on the complement graph of 𝚪. For path graphs P_k, cycle graphs C_ℓ and complete bipartite graphs K_n,m, this article characterizes the embeddability of G(K_n,m) in G(P_k) and in G(C_ℓ).

• 대한수학회논문집
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• 제30권3호
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• pp.313-325
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• 2015

An H-magic labeling in a H-decomposable graph G is a bijection $f:V(G){\cup}E(G){\rightarrow}\{1,2,{\cdots},p+q\}$ such that for every copy H in the decomposition, $\sum{_{{\upsilon}{\in}V(H)}}\;f(v)+\sum{_{e{\in}E(H)}}\;f(e)$ is constant. f is said to be H-V -super magic if f(V(G))={1,2,...,p}. In this paper, we prove that complete bipartite graphs $K_{n,n}$ are H-V -super magic decomposable where $$H{\sim_=}K_{1,n}$$ with $n{\geq}1$.