in this paper, we determine the degree distance of the complement of arbitrary mycielskian graphs. it is well known that almost all graphs have diameter two. we determine this graphical invariant for the mycielskian of graphs with diameter two.

A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph Γ is distance-regular and homogeneous. More precisely, Γ is edge-distance-regular if and only if it is bipartite distance-reg...

Abstract This paper proposes a new method to improve performance of AdaBoost by using a distance weight function to increase the accuracy of its machine learning processes. The proposed distance weight algorithm improves classification in areas where the original binary classifier is weak. This paper derives the new algorithm’s optimal solution, and it demonstrates how classifier accuracy can b...

We survey the problem of comparing labeled trees based on simple local operations of deleting, inserting and relabeling nodes. These operations lead to the tree edit distance, alignment distance and inclusion problem. For each problem we review the results available and present, in detail, one or more of the central algorithms for solving the problem.

A 2-distance k-coloring of a graph G is a mapping from V (G) to the set of colors {1, . . . , k} such that every two vertices at distance at most 2 receive distinct colors. The 2-distance chromatic number χ2(G) of G is then the mallest k for which G admits a 2-distance k-coloring. For any finite set of positive integers D = {d1, . . . , dk}, the integer distance graph G = G(D) is the infinite g...

For many educators, the phrase ‘from distance education to e-learning’ conjures up the view of an ‘evolutionary’ progression beginning with correspondence study and developed through more sophisticated technologies to its current identification with computers, the Internet, and the World Wide Web. For others, particularly those with little knowledge or experience of (and often equally little in...