New classes of clustering coefficient locally maximizing graphs

ON NEW CLASSES OF MULTICONE GRAPHS DETERMINED BY THEIR SPECTRUMS

A multicone graph is defined to be join of a clique and a regular graph. A graph $ G $ is cospectral with graph $ H $ if their adjacency matrices have the same eigenvalues. A graph $ G $ is said to be determined by its spectrum or DS for short, if for any graph $ H $ with $ Spec(G)=Spec(H)$, we conclude that $ G $ is isomorphic to $ H $. In this paper, we present new classes of multicone graphs...

Generating Random Graphs with Tunable Clustering Coefficient

Locally identifying coloring in bounded expansion classes of graphs

A proper vertex coloring of a graph is said to be locally identifying if the sets of colors in the closed neighborhood of any two adjacent non-twin vertices are distinct. The lid-chromatic number of a graph is the minimum number of colors used by a locally identifying vertex-coloring. In this paper, we prove that for any graph class of bounded expansion, the lid-chromatic number is bounded. Cla...

on new classes of multicone graphs determined by their spectrums

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

The Rigidity of New Classes of Graphs

We examine the generic local and global rigidity of various graphs in R. We analyze two classes of graphs that satisfy Hendrickson’s conditions for generic global rigidity, yet fail to be generically globally rigid. We find a large family of bipartite graphs with d > 3, and we use a method that generates infinitely many graphs in R. Finally, we state some conjectures for further exploration.