Even-Odd Cordial Labeling on Join of Zero Divisor Graphs

Balanced Traffic Splitting in Communication Network Using Parity Sum Cordial Labelling of Graphs

Labeling of graph is the assignment of integers to the elements of a graph such as vertices, edges or both. This process gives an easiest way of modelling real world networks. Different types of labeling are available in the literature. Parity sum cordial labeling is a new graph labeling that we defined in this paper....

Antimagic Labeling of Graph Unions of Trees and 4-Cycles

Let $G(V,E)$ be a graph with $V(G)$ as the set of vertices and $E(G)$ as the set of edges. A labeling is a bijection $f:E(G)\to\{1,2,\cdots, |E(G)|\}$. For each vertex \(v\), let \(\phi(v)\) be the sum of the labels on the edges incident to \(v\). If all values \(\phi(v)\) are distinct, the labeling is antimagic, and t...

Trees of odd order with at most two vertices of degree two are edge-graceful

A graph G with q edges and p vertices is edge-graceful if some bijection f from E(G) onto {1,...,q} makes the induced vertex sums f^+(v), the sum of f(e) over the edges e incident to v, distinct modulo p. Lee conjectured in 1989 that every tree of odd order is edge-graceful; the broadest general result we have located,...

Total Neighborhood Prime Labeling of Some Graphs

On the Minimum Coprime Number of Some Graphs

Let G be a finite simple graph. A coprime labeling of G is an injective assignment of positive integers to the vertices such that adjacent vertices receive relatively prime labels. The minimum coprime number of G, denoted by pr(G), is the smallest integer k for which G admits a coprime labeling using labels from {1, 2,...

Directed graphs defined by prime divisors of polynomial values

Let L be the class of all nonconstant polynomials f(x) == Ax2 + Bx + C ∈ Z[x], which are not of the forms Ax2, Bx. We consider the directed graph Gf whose vertex set is P and p → q iff q | f(p), p ̸= q. Let Lf (p) be the set of simple directed paths starting at p and ℓf (p) = sup{|L| : L ∈ Lf (p)}, where |L| is the num...