相关论文: On Perrin Cordial Labeling: A New Approach in Grap…

A \emph{Fibonacci cordial labeling} of a graph \( G \) is an injective function \( f: V(G) \rightarrow \{F_0, F_1, \dots, F_n\} \), where \( F_i \) denotes the \( i^{\text{th}} \) Fibonacci number, such that the induced edge labeling \(…

For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to\{1,2,\cdots,n\}$ is said to be a Legendre cordial labeling modulo $p$, where $p$ is an odd prime, if the induced function $f_p^*:E(G)\to \{0,1\}$, defined by…

Let $p$ be an odd prime. For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to\{1,2,\ldots,n\}$ is said to be a Legendre cordial labeling modulo $p$ if the induced function $f_p^*:E(G)\to \{0,1\}$, defined by $f_p^*…

A $(0,1)$-labelling of a set is said to be {\em friendly} if approximately one half the elements of the set are labelled 0 and one half labelled 1. Let $g$ be a labelling of the edge set of a graph that is induced by a labelling $f$ of the…

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…

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \emph{edge-friendly}. We…

Let $\eta$ be a fixed positive integer. Let $S$ be a subset of $\mathbb{Z}$, $\star:S\times S\to \mathbb{Z}$ be a binary function, and $\zeta_{\eta}:\{\xi\in \mathbb{Z}:\gcd(\xi,\eta)=1\}\to \{0,1\}$ be a function. For a simple connected…

Graph-theoretical labeling provides a rigorous mathematical framework for characterizing the structural and functional organization of complex networks. This paper investigates the application of cordial labeling and signed product cordial…

Hovey introduced $A$-cordial labelings as a generalization of cordial and harmonious labelings \cite{Hovey}. If $A$ is an Abelian group, then a labeling $f \colon V (G) \rightarrow A$ of the vertices of some graph $G$ induces an edge…

A \emph{graceful labeling} of a graph $G$ is an injective function $f : V(G) \to \{0, \ldots, |E(G)|\}$ such that $\{\,|f(u)-f(v)| : uv \in E(G)\,\} = \{1, \ldots, |E(G)|\}$. If such a labeling exists, then we call $G$ \emph{graceful}.…

An undirected graph is said to be cordial if there is a friendly (0,1)-labeling of the vertices that induces a friendly (0,1)-labeling of the edges. An undirected graph $G$ is said to be $(2,3)$-orientable if there exists a friendly…

A graph $G$ is cordial if there exists a function $f$ from the vertices of $G$ to $\{0,1\}$ such that the number of vertices labelled $0$ and the number of vertices labelled $1$ differ by at most $1$, and if we assign to each edge $xy$ the…

A simple and connected $n$-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers $1, 2, 3,\ldots, n$, such that adjacent vertices have relatively prime labels. We will present previously…

We study the question of ``how robust are the known lower bounds of labeling schemes when one increases the number of consulted labels''. Let $f$ be a function on pairs of vertices. An $f$-labeling scheme for a family of graphs $\cF$ labels…

Hovey introduced $A$-cordial labelings as a generalization of cordial and harmonious labelings \cite{Hovey}. If $A$ is an Abelian group, then a labeling $f \colon V (G) \rightarrow A$ of the vertices of some graph $G$ induces an edge…

A simple $n$-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers $1, 2, 3,\ldots, n$ such that adjacent vertices have relatively prime labels. We will present previously unknown prime vertex…

A proper labelling of a graph $G$ is a pair $({\pi},c_{\pi})$ in which ${\pi}$ is an assignment of numeric labels to some elements of $G$, and $c_{\pi}$ is a colouring induced by ${\pi}$ through some mathematical function over the set of…

The sets of vertices and edges of an undirected, simple, finite, connected graph $G$ are denoted by $V(G)$ and $E(G)$, respectively. An arbitrary nonempty finite subset of consecutive integers is called an interval. An injective mapping…

An \emph{adjacency labeling scheme} for a given class of graphs is an algorithm that for every graph $G$ from the class, assigns bit strings (labels) to vertices of $G$ so that for any two vertices $u,v$, whether $u$ and $v$ are adjacent…

Let $p$ be an odd prime and let $F_i$ be the $i$th $(a,b)$-Fibonacci number with initial values $F_0=a$ and $F_1=b$. For a simple connected graph $G=(V,E)$, define a bijective function $f:V(G)\to \{0,1,\ldots,|V|-1\}$. If the induced…