It is well-known that in a directed graph, if deleting any edge will not affect the shortest distance between two specific vertices s and t, then there are two edge-disjoint paths from s to t and both of them are shortest paths. In this paper, we generalize this to shortest k edge-disjoint s-t paths for any positive integer k.

This paper represents a technique for finding optimal paths with multiple indexes in a graph. Up to the present time, all optimal paths have been determined upon one index, say, distance for which an evaluation method exists. In this paper firstly we define multiple indexes for each edge in such a way that anyone can treat the factor for assigning an optimal path. Here, we use Data Envelopment ...

Density and biomass of live trees >10 cm DBHandsaplings 1-9.9 cm DBH, coarse woody debris (LCG—diameter > 10 cm), fine woody debris (LCF — diameter 2.5-9.9 cm), and standing dead trees (>10 cm DBH) were quantified in 56permanent, 1-ha sample plots. These plots are located in four 1(4plots), three 10(12 plots) and two 100(14plots) forestfagments in size and nearby continuous forests (19 plots) a...

We show that the edge-clique graphs of cocktail party graphs have unbounded rankwidth. This, and other observations lead us to conjecture that the edge-clique cover problem is NP-complete for cographs. We show that the independent set problem on edge-clique graphs of cographs and of distance-hereditary graphs can be solved in O(n4) time. We show that the independent set problem on edge-clique g...

an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

A random geometric graph, G(n, r), is formed by choosing n points independently and uniformly at random in a unit square; two points are connected by a straight-line edge if they are at Euclidean distance at most r. For a given constant k, we show that n −k 2k−2 is a distance threshold function for G(n, r) to have a connected subgraph on k points. Based on that, we show that n−2/3 is a distance...

Due to exponential growth of complex data, graph structure has become increasingly important to model various entities and their interactions, with many interesting applications including, bioinformatics, social network analysis, etc. Depending on the complexity of the data, the underlying graph model can be a simple directed/undirected and/or weighted/un-weighted graph to a complex graph (aka ...

Coral reefs and seagrass beds are often located adjacent to one another, but little is known about the degree to which their fish communities are interlinked. To determine whether coral reef fishes on the coral reef are interlinked with or segregated from fishes on adjacent seagrass beds, a 60 m coral reef–seagrass gradient was studied on the island of Zanzibar in the western Indian Ocean. Usin...