We say that a graph G is Class 0 if its pebbling number is exactly equal to its number of vertices. For a positive integer d, let kðdÞ denote the least positive integer so that every graph G with diameter at most d and connectivity at least kðdÞ is Class 0. The existence of the function k was conjectured by Clarke, Hochberg and Hurlbert, who showed that if the function k exists, then it must sa...

Graph energy is defined to be the p -norm of adjacency matrix associated graph for = 1 elaborated as sum absolute eigenvalues matrix. The graph’s spectral radius represents matrix’s largest eigenvalue. Applications energies and radii can found in both molecular computing computer science. On similar lines, Inverse Sum Indeg, ( ISI ) energies, constructed. This article’s main focus generalized s...

A 1993 result of J. Llibre, and M. Misiurewicz, (Theorem A [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. Also a 1980 result of L.S. Block, J. Guckenheimer, M. Misiurewicz and L.S. Young (Lemma 1.5 [3]) states that if G is an A-graph of f then h(G) ? h( f ). In this pap...

A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. ...

Figure 1: Accomplishments of procams-based cybernetics research: (a) Palm interface [8], (b) extended hand interface [5], (c) wearable projection [4], (d) shape deformation interface, (e) deformation visualization, (f) see-through projection and (g) front cover projection for book search support, (h) shadow interface for browsing graphical information on a tabletop [1], (i) shadow pointing, (j)...

A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if either ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 if ( ) ( ) f u f v , then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial ...