This paper presents a novel image representation, which incorporates the principles of Laplacian Pyramid into the irregular graph pyramid. The drawback of the regular Laplacian Pyramid is their lack to keep the topological structure of the image, due to the contraction process in building the Gaussian Pyramid. Irregular graph pyramid is able to hierarchically represent the topological structure...

The transmission TrG(v) of a vertex v connected graph G is the sum distances between and all other vertices in G. stepwise irregular (STI) if |TrG(u) ? TrG(v)| = 1 holds for each edge uv E(G). In this paper, extremal results on STI graphs with respect to size different metric properties are proved. Two families appear cases, balanced complete bipartite odd order so called hatted cycles.

Irregular dynamics in multidimensional systems is commonly associated with chaos. For infinitely large sparse networks of spiking neurons, mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in finite networks of arbitrary connectivity, keeping track of all individual spik...

The hesitant fuzzy graph (HFG) is one of the most powerful tools to find strongest influential person in a network. Many problems practical interest can be modeled and solved by using HFG algorithms. HFGs, belonging FG family, have good capabilities when faced with that cannot expressed FGs. vague-valued (VVHFG) generalization HFG. A VVHFG useful tool various parts, such as meetings, conference...

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 calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...