Designing efficient and reliable wireless mesh-based advanced metering infrastructure
(AMI) networks is challenging. In AMI networks, fine-grained regular data collections from …

An $ L (2, 1) $-labelling of a graph is a function $ f $ from the vertex set to the positive
integers such that $| f (x)-f (y)|\geq 2$ if $ dist (x, y)= 1$ and $| f (x)-f (y)|\geq 1$ if $ dist (x, y) …

In this survey paper we present a general framework for coloring problems that was
introduced in a joint paper which the author presented at WG2003. We show how a number …

An L(p,1)-labeling of a graph is a function f from the vertex set to the positive integers such
that |f(x)-f(y)|\geqslantp if dist (x,y)=1 and |f(x)-f(y)|\geqslant1 if dist (x,y)=2, where dist (x,y) is …

We introduce and study backbone colorings, a variation on classical vertex colorings: Given
a graph G=(V, E) and a spanning subgraph H of G (the backbone of G), a backbone coloring …

Given an integer λ≥ 2, a graph G=(V, E) and a spanning subgraph H of G (the backbone of
G), a λ-backbone coloring of (G, H) is a proper vertex coloring V→{1, 2,…} of G, in which the …

Contributions to Graph Theory Page 1 Contributions to Graph Theory Page 2 The research
described in this thesis was undertaken at the group of Discrete Mathematics and Mathematical …

Consider an undirected graph G and a subgraph H of G, on the same vertex set. The q-
backbone chromatic number BBC q (G, H) is the minimum k such that G can be properly …

An L (p, q)-labeling of a graph G is an assignment f from vertices of G to the set of non-
negative integers {0, 1,…, λ} such that| f (u)− f (v)|≥ p if u and v are adjacent, and| f (u)− f …

We study backbone colorings, a variation on classical vertex colorings: Given a graph G and
a subgraph H of G (the backbone of G), a backbone coloring for G and H is a proper vertex k …