• Honam Mathematical Journal
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• v.27 no.2
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• pp.183-194
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• 2005

A permutation graph is the graph of inversions in a permutation. Here we determine whether a given labelled graph is a permutation graph or not and when a graph is a permutation graph we find the associated permutation. We also characterize all the 2-regular permutation graphs.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.395-408
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• 2015

In present article, we determine the distinguishing number of the merged Johnson graphs which are generalization of both the Kneser graphs and the Johnson graphs.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.487-491
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• 2000

Let G be a covering graph of G. We show that the line graph of G covers the line graph of G. Moreover, if the first covering is regular, then the line-graph covering is regular.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.779-806
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• 2015

We construct a state model for the two-variable Kauman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in $\mathbb{R}^3$.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.577-587
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• 2006

We present several properties concerning infinite maximal planar graphs. Results related to the infinite VAP-free planar graphs are also included. Finally, we extend the result of W. Goddard, who showed that every finite 4-connected maximal planar graph is 4-ordered, to infinite strong triangulations.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.363-373
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• 2023

In this paper we investigate the 4-total mean cordial labeling behavior of arrow graphs, shell-Butterfly graph and graphs obtained by joining two copies of shell graphs by a path.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.827-842
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• 2014

In this paper, we introduce the notion of Cayley intuitionistic fuzzy graphs and investigate some of their properties. We present some interesting properties of intuitionistic fuzzy graphs in terms of algebraic structures. We discuss connectedness in Cayley intuitionistic fuzzy graphs. We also describe different types of ${\alpha}$-connectedness in Cayley intuitionistic fuzzy graphs.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1187-1203
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• 2005

Let g(2n, l, d) be the number of general cubic graphs on 2n labeled vertices with l loops and d double edges. We use inclusion and exclusion with two types of properties to determine the asymptotic behavior of g(2n, l, d) and hence that of g(2n), the total number of general cubic graphs of order 2n. We show that almost all general cubic graphs are connected. Moreover, we determined the asymptotic numbers of general cubic graphs with given connectivity.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.375-382
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• 2017

We exhibit a one-to-one correspondence between 3-colored graphs and subarrangements of certain hyperplane arrangements denoted ${\mathcal{J}}_n$, $n{\in}{\mathbb{N}}$. We define the notion of centrality of 3-colored graphs, which corresponds to the centrality of hyperplane arrangements. Via the correspondence, the characteristic polynomial ${\chi}{\mathcal{J}}_n$ of ${\mathcal{J}}_n$ can be expressed in terms of the number of central 3-colored graphs, and we compute ${\chi}{\mathcal{J}}_n$ for n = 2, 3.

• 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.