If we think of the graph as modeling a network, the vulnerability measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. Many graph theoretical ...

In this paper we discuss about tenacity and its properties in stability calculation. We indicate relationships between tenacity and connectivity, tenacity and binding number, tenacity and toughness. We also give good lower ...

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). ...

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights ...

Let G(V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G) → {0, ...

A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, ...

Let G be a (p,q) graph. An injective map f : E(G) → { ±1,± 2,...,± q} is said to be an edge pair sum labeling if the induced vertex function f *: ...

We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n! Hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the ...

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). ...