Most of recent research works on analyzing wireless LAN (WLAN) traces focused on individual user behaviors [1], [2], [3]. These previous works provide good understandings on WLAN users, and have made vast amount of WLAN traces available to the research community (e.g. from [1], [2], [3], [6]). However, we know from daily lives that we do not make random movement decisions. Usually, WLAN users s...

In this work, we study the signed Roman domination number of the join of graphs. Specially, we determine it for the join of cycles, wheels, fans, and friendship graphs.

A graph G is said to be determined by the spectrum of its Laplacian matrix (DLS) if every with same isomorphic G. In some recent papers it proved that friendship graphs and starlike trees are DLS. If a tree joined merging their vertices degree greater than two, then resulting called path-friendship graph. this paper, graphs, natural generalization trees, also Consequently, using these results w...

In this note, we consider the i-block intersection graphs (i-BIG) of a universal-friend friendship 3-hypergraph and show that they are pancyclic for i = 1, 2. We also show that the 1-BIG of a universalfriend friendship 3-hypergraph is Hamiltonian-connected.

In this paper we provide a purely combinatorial proof of the Friendship Theorem, which has been first proven by P. Erdös et al. by using also algebraic methods. Moreover, we generalize this theorem in a natural way, assuming that every pair of nodes occupies ≥ 2 common neighbors. We prove that every graph, which satisfies this generalized -friendship condition, is a regular graph.

This development provides a formalization of undirected graphs and simple graphs, which are based on Benedikt Nordhoff and Peter Lammich’s simple formalization of labelled directed graphs [4] in the archive. Then, with our formalization of graphs, we have shown both necessary and sufficient conditions for Eulerian trails and circuits [2] as well as the fact that the Königsberg Bridge problem do...

The quadratic embedding constant (QE constant) of a graph is new characteristic value defined through the distance matrix. We derive formulae for QE constants join two regular graphs, double graphs and certain lexicographic product graphs. Examples include complete bipartite wheel friendship completely split graph, some associated to strongly