
Hrnciar and Haviar [3] gave a method to construct a graceful labeling for all trees of diameter at most five. Based on their method and the methods described in Balbuena et al. [1], we shall describe a new construction for gracefully labeled trees by attaching trees to the vertices of a tree admitting a bipartite graceful labeling.
Given two graphs
A
If
In this paper, which is a sequel to the paper entitled `On edge-
A graceful labeling of a graph
Let
We study cube-complementary graphs, that is, graphs whose com- plement and cube are isomorphic. We prove several necessary conditions for a graph to be cube-complementary, describe ways of building new cube-complementary graphs from existing ones, and construct infinite families of cube-complementary graphs.
We suggest the notion of the surface area centered at an edge for a network structure, which generalizes the usual notion of surface area of a structure centered at a vertex. As a specific result, we derive explicit expressions of the edge-centered surface areas for the edge-asymmetric
For a set
The generalized
In this work, we investigate the gap-adjacent-chromatic number, a graph colouring parameter introduced by M. A. Tahraoui, E. Duchéne, and H. Kheddouci in
The main purpose of this work is to state easy colouring approaches for bipartite graphs and to estimate the gap-adjacent-chromatic number for arbitrary graphs in terms of the chromatic number.
We call
For the Firefighter Process with weights on the vertices, we show that the problem of deciding whether a subset of vertices of a total weight can be saved from burning remains NP-complete when restricted to binary trees. In addition, we show that a greedy algorithm that defends the vertex of highest degree adjacent to a burning vertex is not an
Let
We present a simple bijection between the set of triangulations of a convex polygon and the set of
A
For a connected graph
For a nontrivial connected graph
where
For two graphs
An Eulerian graph
An
Analog modulation has served us very well over the years. Digital modulation is an improvement over analog modulation because it provides better bandwidth utilization over analog modulation, less power for signal propagation, it is natural for packet transmission, forward error correction, automatic repeat request, encryption, compression, and signal transformation so that it looks like noise to the adversary. Digital wireless communication is an enormous area that is rapidly growing. Digital communication is a field in which theoretical ideas have had an unusually powerful impact on system design and practice. In this research paper we provide a digital modulation algorithm for efficient transmission based on circular probability distribution theory.
A primitive hypergraph is a hypergraph with maximum cardinality three and maximum degree three such that every
Let
Let
A Stanton-type graph
1970-2025 CP (Manitoba, Canada) unless otherwise stated.