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3.987  Articles
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Phylogenetic trees are representations of the evolutionary descendency of a set of species. In graph-theoretic terms, a phylogenetic tree is a partially labeled tree where unlabeled vertices have at least degree three and labels corresponds to pairwise di... see more

A bipartite graph is called bipancyclic if it contains cycles of every even length from four up to the number of vertices in the graph. A theorem of Schmeichel and Mitchem states that for n?n \geqslant 4, every balanced bipartite graph on 2n2n vertices in... see more

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been studied extens... see more

A Hamiltonian cycle in a connected graph G is defined as a closed walk that traverses every vertex of G exactly once, except the starting vertex at which the walk also terminates. If an edge from a Hamiltonian cycle is removed, it forms a path calleda Ham... see more

Suppose G=(V,E) is a graph with the vertex set V(G) and edge set E(G) we defined a labeling f:V?E?{1,2,…,k} to be an edge irregular total k-labeling of graph G if for every two different edge e and f there is wt(e)?wt(f). The minimum k for which the graph... see more

Relationships of mammals to habitat edges is a continuing concern for conservation as habitat fragmentation continues and ratios of edge to interior habitat increase.  Mammal species that respond negatively to habitat edges may be at greater risk of ... see more

This paper presented a new algorithm for determining the distance of an object in front of a stereo camera placed on a helmet. By using a stereo camera with a Sum of Absolute Difference with a Sobel edge detector, our previous Grid-Edge-Depth map algorith... see more

For an ordered subset S = {v1, …, vk} of vertices in a connected graph G and an edge e' of G, the edge metric S-representation of e'=ab is the vector rGe(e'|S)=(dG(e',v1),…,dG(e',vk)) , where dG(... see more

Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set and E(G) is the edge set. Let k be a natural numbers. For graph G we define a total k-labeling ? such that the vertices of graph G are labeled with {0, 2, 4, . . . , 2kv} a... see more

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