• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.41-53
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• 2023

Let G = (V, E) be a (p, q) graph. Define $${\rho}=\{{\frac{2}{p}},\;{\text{{\qquad} if p is even}}\\{\frac{2}{p-1}},\;{{\text{if p is odd}}$$ and L = {±1, ±2, ±3, … , ±ρ} called the set of labels. Consider a mapping f : V ⟶ L by assigning different labels in L to the different elements of V when p is even and different labels in L 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 difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that ${\mid}{\Delta}_{f_1}-{\Delta}_{f^c_1}{\mid}{\leq}1$, where ${\Delta}_{f_1}$ and ${\Delta}_{f^c_1}$ respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behaviour of Petersen graphs P(n, k) like P(n, 2), P(n, 3), P(n, 4).

• 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 Information Processing Systems
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• v.16 no.1
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• pp.201-209
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• 2020

The graph data structure is popular because it can intuitively represent real-world knowledge. Graph databases have attracted attention in academia and industry because they can be used to maintain graph data and allow users to mine knowledge. Mining reachability relationships between two nodes in a graph, termed reachability query processing, is an important functionality of graph databases. Online traversals, such as the breadth-first and depth-first search, are inefficient in processing reachability queries when dealing with large-scale graphs. Labeling schemes have been proposed to overcome these disadvantages. The state-of-the-art is the 2-hop labeling scheme: each node has in and out labels containing reachable node IDs as integers. Unfortunately, existing 2-hop labeling schemes generate huge 2-hop label sizes because they only consider local features, such as degrees. In this paper, we propose a more efficient 2-hop label size reduction approach. We consider the topological sort index, which is a global feature. A linear combination is suggested for utilizing both local and global features. We conduct experiments over real-world and synthetic directed acyclic graph datasets and show that the proposed approach generates smaller labels than existing approaches.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.173-183
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• 2015

A radio k-labeling f of a graph G is a function f from V (G) to $Z^+{\cup}\{0\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}k+1$ for every two distinct vertices x and y of G, where d(x, y) is the distance between any two vertices $x,y{\in}G$. The span of a radio k-labeling f is denoted by sp(f) and defined as max$\{{\mid}f(x)-f(y){\mid}:x,y{\in}V(G)\}$. The radio k-labeling is a radio labeling when k = diam(G). In other words, a radio labeling is an injective function $f:V(G){\rightarrow}Z^+{\cup}\{0\}$ such that $${\mid}f(x)=f(y){\mid}{\geq}diam(G)+1-d(x,y)$$ for any pair of vertices $x,y{\in}G$. The radio number of G denoted by rn(G), is the lowest span taken over all radio labelings of the graph. When k = diam(G) - 1, a radio k-labeling is called a radio antipodal labeling. An antipodal labeling for a graph G is a function $f:V(G){\rightarrow}\{0,1,2,{\ldots}\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}diam(G)$ holds for all $x,y{\in}G$. The radio antipodal number for G denoted by an(G), is the minimum span of an antipodal labeling admitted by G. In this paper, we investigate the exact value of the radio number and radio antipodal number for the circulant graphs G(4k + 2; {1, 2}).

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.1-14
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• 2024

Let G = (V, E) be a (p, q) graph. Define $$\begin{cases}\frac{p}{2},\:if\:p\:is\:even\\\frac{p-1}{2},\:if\:p\:is\:odd\end{cases}$$ and L = {±1, ±2, ±3, ···, ±ρ} called the set of labels. Consider a mapping f : V → L by assigning different labels in L to the different elements of V when p is even and different labels in L 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 difference cordial labeling if for each edge uv of G there exists a labeling |f(u) - f(v)| such that |Δ_f1 - Δ_f^c1| ≤ 1, where Δ_f1 and Δ_f^c1 respectively denote the number of edges labeled with 1 and number of edges not labeled with 1. A graph G for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of subdivision of some graphs.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.511-524
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• 2023

An L(p₁, p₂, p₃, . . . , p_m)-labeling of a graph G is an assignment of non-negative integers, called as labels, to the vertices such that the vertices at distance i should have at least pi as their label difference. If p₁ = 4, p₂ = 3, p₃ = 2, p₄ = 1, then it is called a L(4, 3, 2, 1)-labeling which is widely studied in the literature. A L(4, 3, 2, 1)-path coloring of graphs, is a labeling g : V (G) → Z⁺ such that there exists at least one path P between every pair of vertices in which the labeling restricted to this path is a L(4, 3, 2, 1)-labeling. This concept was defined and results for some simple graphs were obtained by the same authors in an earlier article. In this article, we study the concept of L(4, 3, 2, 1)-path coloring for complete bipartite graphs, 2-edge connected split graph, Cartesian product and join of two graphs and prove an existence theorem for the same.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.377-387
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• 2014

Let G be a (p, q) graph. Let f be a map from V (G) to {1, 2, ${\ldots}$, p}. For each edge uv, assign the label ${\mid}f(u)-f(\nu){\mid}$. f is called a difference cordial labeling if f is a one to one map and ${\mid}e_f(0)-e_f(1){\mid}{\leq}1$ where $e_f(1)$ and $e_f(0)$ denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph with admits a difference cordial labeling is called a difference cordial graph. In this paper, we investigate the difference cordial labeling behavior of triangular snake, Quadrilateral snake, double triangular snake, double quadrilateral snake and alternate snakes.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.59-74
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• 2017

A radio labeling of a graph G is a function $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ with the property that ${\mid}f(u)-f(v){\mid}{\geq}1+diam(G)-d(u,v)$ for every pair of vertices $u,v{\in}V(G)$, where diam(G) and d(u, v) are diameter and distance between u and v in the graph G respectively. The radio number of a graph G, denoted by rn(G), is the smallest integer k such that G admits a radio labeling. In this paper, we completely determine radio number of all transformation graphs of a path.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.279-301
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• 2017

An L(3, 2, 1)-labeling for the graph G = (V, E) is an assignment f of a label to each vertices of G such that ${\mid}f(u)-f({\upsilon}){\mid}{\geq}4-k$ when $dist(u,{\upsilon})=k{\leq}3$. The L(3, 2, 1)-labeling number, denoted by ${\lambda}_{3,2,1}(G)$, for G is the smallest number N such that there is an L(3, 2, 1)-labeling for G with span N. In this paper, we compute the L(3, 2, 1)-labeling number ${\lambda}_{3,2,1}(G)$ when G is a cylindrical grid, which is the cartesian product $P_m{\Box}C_n$ of the path and the cycle, when $m{\geq}4$ and $n{\geq}138$. Especially when n is a multiple of 4, or m = 4 and n is a multiple of 6, then we have ${\lambda}_{3,2,1}(G)=11$. Otherwise ${\lambda}_{3,2,1}(G)=12$.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.451-465
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• 2016

A Radio labeling of the graph G is a function g from the vertex set V (G) of G to ℤ⁺ such that |g(u) - g(v)| ≥ diam(G) + 1 - d_G(u, v), where diam(G) and d(u, v) are diameter and distance between u and v in graph G respectively. The radio number rn(G) of G is the smallest number k such that G has radio labeling with max{g(v) : v ∈ V(G)} = k. We investigate radio number for some families of generalized caterpillar graphs.