• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.149-156
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• 2019

Let G be a (p, q) graph. Let $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ be a map where $k{\in}{\mathbb{N}}$ and k > 1. For each edge uv, assign the label gcd(f(u), f(v)). f is called k-Total prime cordial labeling of G if ${\mid}t_f(i)-t_f(j){\mid}{\leq}1$, $i,j{\in}\{1,2,{\ldots},k\}$ where $t_f$(x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of some graphs.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.227-237
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• 2016

In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v_f (i) − v_f (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e_f (0) − e_f (1)| ≤ 1 where v_f (x) denotes the number of vertices labeled with x, e_f (1) and e_f (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.171-184
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• 2024

In this paper, we show that if G is strongly regular then the Gallai graph Γ(G) and the anti-Gallai graph ∆(G) of G are edge-regular. We also identify conditions under which the Gallai and anti-Gallai graphs are themselves strongly regular, as well as conditions under which they are 2-connected. We include also a number of concrete examples and a discussion of spectral properties of the Gallai and anti-Gallai graphs.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.9-14
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• 2007

A signed 3-partite graph is a 3-partite graph in which each edge is assigned a positive or a negative sign. Let G(U, V, W) be a signed 3-partite graph with $U\;=\;\{u_1,\;u_2,\;{\cdots},\;u_p\},\;V\;=\;\{v_1,\;v_2,\;{\cdots},\;v_q\}\;and\;W\;=\;\{w_1,\;w_2,\;{\cdots},\;w_r\}$. Then, signed degree of $u_i(v_j\;and\;w_k)$ is $sdeg(u_i)\;=\;d_i\;=\;d^+_i\;-\;d^-_i,\;1\;{\leq}\;i\;{\leq}\;p\;(sdeg(v_j)\;=\;e_j\;=\;e^+_j\;-\;e^-_j,\;1\;{\leq}\;j\;{\leq}q$ and $sdeg(w_k)\;=\;f_k\;=\;f^+_k\;-\;f^-_k,\;1\;{\leq}\;k\;{\leq}\;r)$ where $d^+_i(e^+_j\;and\;f^+_k)$ is the number of positive edges incident with $u_i(v_j\;and\;w_k)$ and $d^-_i(e^-_j\;and\;f^-_k)$ is the number of negative edges incident with $u_i(v_j\;and\;w_k)$. The sequences ${\alpha}\;=\;[d_1,\;d_2,\;{\cdots},\;d_p],\;{\beta}\;=\;[e_1,\;e_2,\;{\cdots},\;e_q]$ and ${\gamma}\;=\;[f_1,\;f_2,\;{\cdots},\;f_r]$ are called the signed degree sequences of G(U, V, W). In this paper, we characterize the signed degree sequences of signed 3-partite graphs.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.197-201
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• 2014

In this paper, we study some properties of finite or infinite poset P determined by properties of the ideal based zero-divisor graph properties $G_J(P)$, for an ideal J of P.

• International conference on construction engineering and project management
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• 2022.06a
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• pp.800-807
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• 2022

This study aims to review the use of graph databases in construction research. Based on the diagnosis of the current research status, a future research direction is proposed. The use of graph databases in construction research has been increasing because of the efficiency in expressing complex relations between entities in construction big data. However, no study has been conducted to review systematically the status quo of graph databases. This study analyzes 42 papers in total that deployed a graph model and graph database in construction research, both quantitatively and qualitatively. A keyword analysis, topic modeling, and qualitative content analysis were conducted. The review identified the research topics, types of data sources that compose a graph, and the graph database application methods and algorithms. Although the current research is still in a nascent stage, the graph database research has great potential to develop into an advanced stage, fused with artificial intelligence (AI) in the future, based on the active usage trends this study revealed.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.223-237
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• 2021

Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.505-519
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• 2023

Let G = (V, E) be a graph. A subset S of V is called a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating sets of G. A dominating set S is called a connected dominating set if the subgraph induced by S is connected. The minimum cardinality taken over all connected dominating sets of G is called the connected domination number of G, and is denoted by γ_c(G). In this paper, we investigate the Nordhaus-Gaddum type results for the connected domination number and its derived graphs like line graph, subdivision graph, power graph, block graph and total graph, and characterize the extremal graphs.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.2
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• pp.415-420
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• 2016

A graph G=(V,E) is called an interval graph with a set V of vertices representing intervals on a line such that there is an edge $(i,j){\in}E$ if and only if intervals i and j intersect. In this paper, we are concerned in the vertex connectivity, one of various characteristics of the graph. Specifically, the vertex connectivity of an interval graph is represented by the overlapping of intervals. Also we propose an efficient algorithm to compute the vertex connectivity on the fully dynamic environment in which the vertices or the edges are inserted or deleted. Using a special kind of interval tree, we show how to compute the vertex connectivity and to maintain the tree in O(logn) time when a new interval is added or an existing interval is deleted.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.391-402
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• 2022

For a given graph G = (V, E), a dominating set is a subset V' of the vertex set V so that each vertex in V ＼ V' is adjacent to a vertex in V'. The minimum cardinality of a dominating set of G is called the domination number of G and is denoted by γ(G). For an integer k ≥ 1, the k-th power G^k of a graph G with V (G^k) = V (G) for which uv ∈ E(G^k) if and only if 1 ≤ d_G(u, v) ≤ k. Note that G² is the square graph of a graph G. In this paper, we obtain some tight bounds for the sum of the domination numbers of a graph and its square graph in terms of the order, order and size, and maximum degree of the graph G. Also, we characterize such extremal graphs.