• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.285-294
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• 2021

In the present work we introduce Gaussian vertex prime labeling and investigate Gaussian vertex prime labeling for gear graph, book graph, wheel graph, kayak paddle, one point union of gear graph and one point union of wheel graph.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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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.

• 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.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.89-100
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• 2015

In this paper, we present exact formulae for the multiplicatively weighted Harary indices of join, tensor product and strong product of graphs in terms of other graph invariants including the Harary index, Zagreb indices and Zagreb coindices. Finally, We apply our result to compute the multiplicatively weighted Harary indices of fan graph, wheel graph and closed fence graph.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.313-323
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• 2007

The equitable total chromatic number ${\chi}_{et}(G)$ of a graph G is the smallest integer ${\kappa}$ for which G has a total ${\kappa}$-coloring such that the number of vertices and edges in any two color classes differ by at most one. In this paper, we determine the equitable total chromatic number of one class of the graphs.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.1059-1075
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• 2019

Let G be a graph with no isolated vertex. A total dominating set, abbreviated TDS of G is a subset S of vertices of G such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a TDS of G. In this paper, we study the total domination number of central graphs. Indeed, we obtain some tight bounds for the total domination number of a central graph C(G) in terms of some invariants of the graph G. Also we characterize the total domination number of the central graph of some families of graphs such as path graphs, cycle graphs, wheel graphs, complete graphs and complete multipartite graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total domination number of central graphs.

• Journal of Fisheries and Marine Sciences Education
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• v.21 no.4
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• pp.586-591
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• 2009

The marine traffic accidents go on increasing owing to the increment of marine traffic capacity, and the solutions about these matters are vigorously considering by many researchers. When the watch officer navigates to the narrow channel, bend or an area obscured by an intervening obstruction and around the harbour limit he must follow the planned track. The watch officer can safely navigate along the course laid down only when he alters his course in advance before the new course distance earlier than the course alternation point. If we call this point to be changed in advance a turning bearing, the turning bearing is decided according to the direction and the range from the clearing objects. The turning bearing helps the watch officer to determine whether the ship is at wheel-over position or not. The author in this paper suggest how to make and use a curve graph which is decided according to the direction and the distance from the clearing objects. If the watch officer utilize this curve graph he can judge swiftly and precisely whether his ship is at the wheel - over position or not.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.149-156
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• 2006

The circular list coloring is a circular version of list colorings of graphs. Let $\chi_{c,l}$ denote the circular choosability(or the circular list chromatic number). In this paper, the circular choosability of outer planar graphs and odd wheel is discussed.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.497-506
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• 2021

Let G be a graph. Let f : V (G) → {0, 1, …, k - 1} be a function where k ∈ ℕ and k > 1. For each edge uv, assign the label $f(uv)={\lceil}{\frac{f(u)+f(v)}{2}}{\rceil}$. f is called k-total mean cordial labeling of G if ${\mid}t_{mf}(i)-t_{mf}(j){\mid}{\leq}1$, for all i, j ∈ {0, 1, …, k - 1}, where t_mf (x) denotes the total number of vertices and edges labelled with x, x ∈ {0, 1, …, k-1}. A graph with admit a k-total mean cordial labeling is called k-total mean cordial graph.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.55-69
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• 2024

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} && p\;\text{is even} \\ {\frac{p-1}{2}} && p\;\text{is odd,}}$$ and M = {±1, ±2, … ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{s}}_{{\lambda}_1}-\bar{\mathbb{s}}_{{\lambda}^c_1}{\mid}\,{\leq}\,1$ where $\bar{\mathbb{s}}_{{\lambda}_1}$ and $\bar{\mathbb{s}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of some union of graphs.