a special class of cubic graphs are the cycle permutation graphs. a cycle permutation graph pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.in this paper we determine a good upper bound for tenacity of cycle permutation graphs.

the total version of geometric–arithmetic index of graphs is introduced based on the endvertexdegrees of edges of their total graphs. in this paper, beside of computing the total gaindex for some graphs, its some properties especially lower and upper bounds are obtained.

A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph. We introduce and study the class of connected-domishold graphs, which are graphs that admit non-negative real weights associated to their vertices such that a set of vertices is a connected dominating set if and only if the sum of the corresponding weights exceeds a certain threshold. We sho...

It is well-known that many NP-hard problems can be solved efficiently on graphs of bounded treewidth. We begin by showing that Knuth’s results on nested satisfiability are easily derived from this fact since nested satisfiability graphs have treewidth at most three. Noting that nested satisfiability graphs have a particular form of planar drawing, we define a more general form of graph drawing ...

Treatment of general structured information by neural networks is an emerging research topic. Here we show how representations for graphs preserving all the information can be devised by Recursive Principal Components Analysis learning. These representations are derived from eigenanalysis of extended vectorial representations of the input graphs. Experimental results performed on a set of chemi...

Dr. Lu made major contributions to the theory of large sparse random graphs — a new direction in graph theory for modeling many real-world graphs. Together with Chung (and other collaborators), Lu introduced and studied several random graph models, including models using preferential attachment scheme, partial duplication models, random graphs with expected degree sequence, and hybrid models. T...

Random graphs with high probability satisfy the n-e.c. adjacency property, although until recently few explicit examples of such graphs were known. We supply a new general construction for generating infinite familes of finite regular n-e.c. graphs derived from certain resolvable Steiner 2-designs. We supply an extension of our construction to the infinite case, and thereby give a new represent...

the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...

we study the set of all determinants of adjacency matrices of graphs with a given number of vertices. using brendan mckay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. using an idea of m. newman, it is proved that if $...

It is conjectured that connected graphs with given number of vertices and minimum spectral gap (i.e., the difference between their two largest eigenvalues) are double kite graphs. The conjecture is confirmed for connected graphs with at most 10 vertices, and, using variable neighbourhood metaheuristic, there is evidence that it is true for graphs with at most 15 vertices. Several spectral prope...