• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.519-524
• /
• 2007

Facility location problems deal with the concept of centrality and centrality questions are examined using graphs and eccentricity. In this paper, we give interesting properties of a tree in relation with the number of central vertices and peripheral vertices. Also we have some conditions to be an eccentric graph in terms of the girth of a graph.

• Journal of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1141-1154
• /
• 2014

A k-hypertournament H on n vertices, where $2{\leq}k{\leq}n$, is a pair H = (V,A), where V is the vertex set of H and A is a set of k-tuples of vertices, called arcs, such that for all subsets $S{\subseteq}V$ with |S| = k, A contains exactly one permutation of S as an arc. Recently, Li et al. showed that any strong k-hypertournament H on n vertices, where $3{\leq}k{\leq}n-2$, is vertex-pancyclic, an extension of Moon's theorem for tournaments. In this paper, we prove the following generalization of another of Moon's theorems: If H is a strong k-hypertournament on n vertices, where $3{\leq}k{\leq}n-2$, and C is a Hamiltonian cycle in H, then C contains at least three pancyclic arcs.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.387-401
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.25 no.1_2
• /
• pp.155-167
• /
• 2007

A graph G is called to be a 2-degree integral subgraph of a q-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactly q - 1 triangles. An added-vertex q-tree G with n vertices is obtained by taking two vertices u, v (u, v are not adjacent) in a q-trees T with n - 1 vertices such that their intersection of neighborhoods of u, v forms a complete graph $K_{q}$, and adding a new vertex x, new edges xu, xv, $xv_{1},\;xv_{2},\;{\cdots},\;xv_{q-4}$, where $\{v_{1},\;v_{2},\;{\cdots},\;v_{q-4}\}\;{\subseteq}\;K_{q}$. In this paper we prove that a graph G with minimum degree not equal to q - 3 and chromatic polynomial $$P(G;{\lambda})\;=\;{\lambda}({\lambda}-1)\;{\cdots}\;({\lambda}-q+2)({\lambda}-q+1)^{3}({\lambda}-q)^{n-q-2}$$ with $n\;{\geq}\;q+2$ has and only has 2-degree integral subgraph of q-tree with n vertices and added-vertex q-tree with n vertices.

• Journal of the Korean Mathematical Society
• /
• v.42 no.6
• /
• pp.1251-1264
• /
• 2005

Let D be an acyclic digraph. The competition graph of D has the same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that (u, x) and (v, x) are arcs of D. The competition number of a graph G, denoted by k(G), is the smallest number k such that G together with k isolated vertices is the competition graph of an acyclic digraph. It is known to be difficult to compute the competition number of a graph in general. Even characterizing the graphs with competition number one looks hard. In this paper, we continue the work done by Cho and Kim[3] to characterize the graphs with one hole and competition number one. We give a sufficient condition for a graph with one hole to have competition number one. This generates a huge class of graphs with one hole and competition number one. Then we completely characterize the graphs with one hole and competition number one that do not have a vertex adjacent to all the vertices of the hole. Also we show that deleting pendant vertices from a connected graph does not change the competition number of the original graph as long as the resulting graph is not trivial, and this allows us to construct infinitely many graph having the same competition number. Finally we pose an interesting open problem.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.1-23
• /
• 2005

The shortest-paths problem is a fundamental problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one vertex to another often gives the best way to route a message between the vertices. This paper presents an $O(n^2)$ time sequential algorithm and an $O(n^2/p+logn)$ time parallel algorithm on EREW PRAM model for solving all pairs shortest paths problem on circular-arc graphs, where p and n represent respectively the number of processors and the number of vertices of the circular-arc graph.

• Journal of electromagnetic engineering and science
• /
• v.13 no.1
• /
• pp.16-21
• /
• 2013

This study presents the angular effects of virtual vertices inserted for effective treatment of the boundary edge laid on an infinite conducting surface in a half-space scattering problem. We investigated the angular effects of virtual vertices by first computing the radar cross section (RCS) of a specific scatterer; i.e., a tilted conducting plate in contact with the ground surface, by inserting the virtual vertex in half-space. Here, the electric field integral equation is used to solve this problem with various virtual vertex angles (${\theta}_{\nu}$) and conducting plate inclination angles (${\theta}_r$) ranging from $0^{\circ}$ to $180^{\circ}$. The effects of the angles ${\theta}_{\nu}$ and ${\theta}_r$ on the RCS computation are clearly shown with numerical results with and without the virtual vertices in free- and half-spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.543-558
• /
• 2013

Let ${\Gamma}$ be a graph which contains two vertices $a$, $b$ with the same link. For the case where the link has less than 3 vertices, we prove that if the right-angled Artin group A(${\Gamma}$) contains a hyperbolic surface subgroup, then A(${\Gamma}$-{a}) contains a hyperbolic surface subgroup. Moreover, we also show that the same result holds with certain restrictions for the case where the link has more than or equal to 3 vertices.

• Journal of applied mathematics & informatics
• /
• v.35 no.1_2
• /
• pp.95-111
• /
• 2017

Recently, interval-valued fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in [0.1] rather than the crisp values between 0 and 1. In this paper, we introduce the concepts of regular and totally regular interval-valued fuzzy graphs and discusses some properties of the ${\mu}$-complement of interval-valued fuzzy graph. Self ${\mu}$-complementary interval-valued fuzzy graphs and self-weak ${\mu}$-complementary interval-valued fuzzy graphs are defined and a necessary condition for an interval valued fuzzy graph to be self ${\mu}$-complementary is discussed. We define busy vertices and free vertices in interval valued fuzzy graph and study their image under an isomorphism.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.119-139
• /
• 2022

This paper deals with the λ-labeling and L(2, 1)-coloring of simple graphs. A λ-labeling of a graph G is any labeling of the vertices of G with different labels such that any two adjacent vertices receive labels which differ at least two. Also an L(2, 1)-coloring of G is any labeling of the vertices of G such that any two adjacent vertices receive labels which differ at least two and any two vertices with distance two receive distinct labels. Assume that a partial λ-labeling f is given in a graph G. A general question is whether f can be extended to a λ-labeling of G. We show that the extension is feasible if and only if a Hamiltonian path consistent with some distance constraints exists in the complement of G. Then we consider line graph of bipartite multigraphs and determine the minimum number of labels in L(2, 1)-coloring and λ-labeling of these graphs. In fact we obtain easily computable formulas for the path covering number and the maximum path of the complement of these graphs. We obtain a polynomial time algorithm which generates all Hamiltonian paths in the related graphs. A special case is the Cartesian product graph K_n☐K_n and the generation of λ-squares.