Search

Topological indices M1/M2 known as first/second Zagreb indices are defined as the sum of the sum/product of degrees of pairs of adjacent vertices of a simple graph. These indices and their properties have been studied in detail under chemical graph theory. In this paper we introduce the concepts of first, second and hyper Zagreb indices of fuzzy graphs. We also study the Zagreb matrices and the associated Zagreb energies of fuzzy graphs. Some bounds for these energies are also obtained.

Let f: V (G) → {1, 2, . . ., n} be a bijection for a graph G of order n. The weight of a vertex v of G denoted by w(v) is defined as sum of labels of all vertices adjacent to vertex v in G. If w(u) ̸= w(v) for every pair of distinct vertices u, v ∈ V (G) then labeling f is called distance antimagic. Any graph G which admits such a labeling is called a distance antimagic graph. In this paper, we determine the distance antimagic labeling of Kneser graph K(2n, n), bipartite Kneser graph H(2n+1, n) using computer-aided algorithm. We investigate the existence of distance antimagic labeling for cycle related graphs having application in surveillance systems of civil engineering and urban planning and verify that vertex weights are distinct using computer algorithm. Also, we present some families of disconnected graphs that admit distance antimagic labeling and later show that Kneser graph K(n, 2) does not admit (a, d)-distance antimagic labeling. [ABSTRACT FROM AUTHOR]