A study on the varieties of equivalent cordial labeling graphs

Graph labeling is the term used to describe the procedure of giving unique identifiers. Graph attributing is a method for modeling real-world problems in industries such as circuit design, surveillance technology, and telecommunications networks. A graph is characterized as possessing cubic roots cordial labeling if each node is designated with either the value 1, δ or δ2 or another specified integer. The derived set containing the value 1 or another integer, the mathematical conditions η (k) − η (w)| ≤ 1 and | ξ (k) − ξ (w)| ≤ 1, k ≠ w and k, w ∈ {1, δ, δ2} where η (k) and ξ (k) are represents the aggregated vertices and edges assigned in k ∈ {1, δ, δ2}. Labeled graphs prove to be immensely beneficial across a variety of mathematical frameworks, including domains such as cyber security and radar code formulation. The application of cordial labeling has been demonstrated to provide significant advantages in the context of signal processing channels and challenges associated with specific code word design. The idea of cubic roots cordial labeling has attracted a lot of academic attention among various labeling techniques, unique structural characteristics and capacity to depict a fair flow of information within linked networks. The investigation of the behavior of cubic roots cordial labeling in relation to graph operations is currently receiving extensive scholarly examination, particularly concerning path graphs, despite its critical relevance. This paper explore the cordial labeling of cubic product graphs generated from the combination of two path graphs. The four fundamental graph operations on which we particularly focus on activities, we analyze the specific conditions to possess cubic roots cordial labeling.

The computational complexity of cordial and equitable labelling

The product cordial labeling is a variant of cordial labeling. Here we investigate product cordial labelings for alternate triangular snake and alternate quadrilateral snake graphs.

Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate the 3-difference cordial labeling of wheel, helms, flower graph, sunflower graph, lotus inside a circle, closed helm, and double wheel.

In graph theory, labeling of vertices and edges according to specific rules offers insight into the structural properties of graphs and their potential applications. This study focuses on a particular type of graph labeling known as Super Lehmer-3 Mean Labeling. A graph is said to admit such a labeling if there exists an injective vertex labeling such that the corresponding edge labels, derived from the Lehmer-3 mean of their incident vertex labels, are also distinct and satisfy certain arithmetic conditions. Graphs that admit such a labeling are termed Super Lehmer-3 Mean Graphs.In this work, we investigate the existence of super Lehmer-3 mean labeling in various families of theta-related graphs. Specifically, we analyze standard theta graphs and their structural variations obtained by subdivisions and attachments of pendant vertices. The results confirm that these modified forms of theta graphs also admit super Lehmer-3 mean labeling. Additionally, we extend our exploration to harmonic mean labeling in selected theta graphs, highlighting the conditions under which this alternative labeling scheme is valid.The findings presented in this paper contribute to the growing body of knowledge in graph labeling theory, offering new characterizations and constructions of labeled graph families. These results may have implications for theoretical studies and applications where such labeling structures are relevant.

Characterization of graph properties for improved Pareto fronts using heuristics and EA for bi-objective graph coloring problem

An elementary net system is the basic system model of net theory. The state space of an elementary net system is formalized through the notion of the case graph, which is an edge-labeled graph with a distinguished initial node. The paper investigates syntactic, i.e., graph theoretic properties of case graphs of elementary net systems. In particular it studies the structure of isomorphisms between case graphs.

The process of assigning the binary numbers 0 and 1 to the edges of a graph \(G = (V, E)\) through evaluating functions defined on the vertex set V and the edge set E of G using the concepts of prime and Narayana numbers by satisfying cordiality on the edges. This process on the graph G is known as Narayana prime cordial labeling of G and this graph G is called Narayana prime cordial graph. In this article, we compute the Narayana prime cordial labeling of Web graphs and Flower graphs.

A (0; 1)-labeling of a set is said to be friendly if the number of elements of the set labeled 0 and the number labeled 1 differ by at most 1. Let g be a labeling of the edge set of a graph that is induced by a labeling f of the vertex set. If both g and f are friendly then f is said to be a cordial labeling of the graph. This concept extended to directed graphs is called (2; 3)-cordiality of digraphs. We investigate the labelings that are both cordial for a graph and (2; 3)-cordial for an orientation of it. We also consider the same problem for other known binary vertex labelings of graphs.

A mapping f:V(G)→{0,1,2} is called a 3-product cordial labeling if |vf(i)−vf(j)|≤1 and |ef(i)−ef(j)|≤1 for any i,j∈{0,1,2}, where vf(i) denotes the number of vertices labeled with i,ef(i) denotes the number of edges xy with f(x)f(y)≡i(mod 3). A graph with a 3-product cordial labeling is called a 3-product cordial graph. In this paper, we investigate the 3-product cordial behaviour for some standard graphs.

Cordial labeling of hypertrees

This study investigates the application of Smarandache product cordial labeling techniques to Christmas tree graphs. Graph labeling is a crucial aspect of graph theory, with applications in various fields such as computer science, coding theory, and network design. Smarandache product cordial labeling, in particular, offers a unique approach to labeling graphs while maintaining specific properties. By exploring the application of these techniques to Christmas tree graphs, this research aims to contribute to the understanding of graph labeling and its potential applications in real-world problems. The study presents theoretical results, algorithmic approaches, and potential extensions to related graph structures.

This papers deals with the Edge cordial labeling of newly introduced eight sprocket graph. This graph is already proven as cordial and gracious in graph labelling. In our study we have further proved that Eight Sprocket graph related families of connected edge-cordial graphs. Also the path union of Eight Sprocket graph, cycle of Eight Sprocket graph and star of Eight Sprocket graph are Edge-cordial.Â

Planarity can be verified by an approximate proof labeling scheme in constant-time

In this paper, we present the graceful labeling of open cyclic grid graph and vertex cordial labeling of generalized open cyclic grid graph.