Wireless sensor networks are often located in areas where access to them is difficult or dangerous. Today, in wireless sensor networks, cluster-based routing protocols by dividing sensor nodes into distinct clusters and selecting local head-clusters to combine and send information of each cluster to the base station and balanced energy consumption by network nodes, get the best performance ...

The human brain is a complex system consist of connected nerve cells that adapts with and learn from the environment by changing its regional activities. Synchrony between these regional activities called functional network changes during the life, and with learning of new skills. Time perception and interval discrimination are among the most necessary skills for the human being to perceive mot...

For a connected graph G of order p ≥ 2 and a vertex x of G, a set S ⊆ V (G) is an x-monophonic set of G if each vertex v ∈ V (G) lies on an x− y monophonic path for some element y in S. The minimum cardinality of an x-monophonic set of G is defined as the x-monophonic number of G, denoted by mx(G). An x-monophonic set of cardinality mx(G) is called a mx-set of G. We determine bounds for it and ...

The path-distance-width of a connected graph G is the minimum integer w satisfying that there is a nonempty subset of S ⊆ V (G) such that the number of the vertices with distance i from S is at most w for any nonnegative integer i. In this note, we determine the path-distance-width of hypercubes.

We showed in [4] that every connected graph can be realized as the cut locus of some point on some riemannian surface S. Here, criteria for the orientability of S are given, and are applied to classify the distinct, orientable, cut locus structures on graphs with four generating cycles. Math. Subj. Classification (2000): — 53C22, 05C10

We investigate embeddings of graphs on orientable 2-dimensional surfaces such that all face boundaries have fewer edges than every noncontractible cycle. We show that such embeddings are always minimum genus embeddings and that they share many properties with planar embeddings. For example, if the graph is 3-connected, then the embedding is unique. We use this to obtain a polynomially bounded a...

For an integer s > 0 and for u, v ∈ V (G) with u = v, an (s; u, v)-pathsystem of G is a subgraph H of G consisting of s internally disjoint (u, v)-paths, and such an H is called a spanning (s; u, v)-path system if V (H) = V (G). The spanning connectivity κ∗(G) of graph G is the largest integer s such that for any integer k with 1 ≤ k ≤ s and for any u, v ∈ V (G) with u = v, G has a spanning (k;...

Let G be a connected graph. An unordered pair {x, y} of vertices of G is a resolving pair if no vertex of G has the same distance to x and y. It was conjectured in [8] that the number of resolving pairs of a connected graph of order n is bounded above by bn2 4 c. In this note we show that there exists a constant c > 0 such that for sufficiently large n every graph of order n contains at most ( ...