This paper presents the Graph Analytics Repository for Designing Next-generation Accelerators (GARDENIA), a benchmark suite for studying irregular algorithms on massively parallel accelerators. Existing generic benchmarks for accelerators have mainly focused on high performance computing (HPC) applications with limited control and data irregularity, while available graph analytics benchmarks do...

We consider only finite undirected graphs without loops or multiple edges. For terminology and notation not defined here we refer the reader to Bondy and Murty’s textbook [6]. In this note we investigate irregularity measures of graphs. A graph is regular if all its vertices have the same degree, otherwise it is irregular. However, it is of interest to measure how irregular it is. Several appro...

A graph G = (V,E) with p vertices and q edges is said to be a total mean cordial graph if there exists a function f : V (G) → {0, 1, 2} such that f(xy) = [(f(x)+f(y))/2] where x, y ∈ V (G), xy ∈ E(G), and the total number of 0, 1 and 2 are balanced. That is |evf (i) − evf (j)| ≤ 1, i, j ∈ {0, 1, 2} where evf (x) denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). In thi...

A balanced coloring of a graph G means a triple {P1, P2,X} of mutually disjoint subsets of the vertex-set V (G) such that V (G) = P1⊎P2⊎X and |P1| = |P2|. A balanced decomposition associated with the balanced coloring V (G) = P1⊎P2⊎X of G is defined as a partition of V (G) = V1⊎· · ·⊎Vr (for some r) such that, for every i ∈ {1, · · · , r}, the subgraphG[Vi] of G is connected and |Vi∩P1| = |Vi∩P...

The balanced Hamiltonian cycle problem is a quiet new topic of graph theorem. Given a graph G = (V, E), whose edge set can be partitioned into k dimensions, for positive integer k and a Hamiltonian cycle C on G. The set of all i-dimensional edge of C, which is a subset by E(C), is denoted as Ei(C). If ||Ei(C)| |Ej(C)|| 1 for 1 i < j k, C is called a balanced Hamiltonian cycle. In this paper, th...

In this paper, we discuss balanced bipolar intuitionistic fuzzy graphs and study some of their properties 1.Introduction Graph theory is developed when Euler gave the solution to the famous Konigsberg bridge problem in 1736. Graph theory is very useful as a branch of combinatorics in the field of geometry, algebra, number theory, topology, operations research, optimization and computer science....