Total Neighborhood Prime Labeling of Some Graphs

On Prime Labeling of Some Union Graphs and Circulant Graphs

Packing and Covering Cycles Through Prescribed Vertices

Let $G$ be a finite simple graph and let $S\subseteq V(G)$. We prove that the minimum number of vertices meeting every cycle that intersects $S$ is at most the maximum number of vertices of $S$ covered by a collection of vertex-disjoint cycles. This answers a question posed by Bowler, Ghorbani, Gut, Jacobs, and Reich [...

Prime Labelings of Trees

A prime labeling of a graph labels its vertices bijectively with the integers from one to the number of vertices, so that adjacent vertices receive coprime labels. I prove the Entringer-Tout conjecture that every tree admits a prime labeling, extending the result of Haxell, Pikhurko, and Taraz from sufficiently large t...

Antimagicness of join graphs

An antimagic labelling of a graph G = (V,E) is a bijection from E to {1,2,...,|E|}, such that all vertex-sums are pairwise distinct, where the vertex-sum of each vertex is the sum of labels over edges incident to this vertex. A graph is antimagic if it has an antimagic labelling. Hartsfield and Ringel in 1990 stated th...

Even-Odd Cordial Labeling on Join of Zero Divisor Graphs

Let G(V,E) be a graph, and let f: V(G) →{1,2,….|𝑉(𝐺)|} be a bijective vertex labeling. The induced edge labeling f*: E(G) → {0,1} is defined by assigning the label 1 to an edge uv whenever the labels f(u) and f(v) have same parity, and the label 0 whenever they have different parities. If the difference between the num...

Theory & Applications of Graphs Theory & Applications of Graphs

This work establishes general properties of k -total bondage and finds exact values for certain graph classes including paths, cycles, wheels, complete and complete bipartite graphs.