This paper is concerned with the general atom-bond sum-connectivity index ABSγ, which a generalization of recently proposed index, where γ any real number. For connected graph G more than two vertices, number ABSγ(G) defined as sum (1−2(dx+dy)−1)γ over all edges xy G, dx and dy represent degrees vertices x y respectively. −10≤γ≤10, significance ABSγ examined on data set twenty-five benzenoid hy...

A connected graph G is said to be a cactus if any two cycles have at most one vertex in common. The multiplicative sum Zagreb index of the product degrees adjacent vertices G. In this paper, we introduce several transformations that are useful tools for study extremal properties index. Using these and symmetric structural representations some graphs, determine graphs having maximal with prescri...

On Sum Coloring of Graphs Mohammadreza Salavatipour Master of Science Graduate Department of Computer Science University of Toronto 2000 The sum coloring problem asks to nd a vertex coloring of a given graph G, using natural numbers, such that the total sum of the colors of vertices is minimized amongst all proper vertex colorings of G. This minimum total sum is the chromatic sum of the graph, ...

We determine the minimum sum–connectivity index of bicyclic graphs with n vertices and matching number m, where 2 ≤ m ≤ ⌊n2 ⌋, the minimum and the second minimum, as well as the maximum and the second maximum sum–connectivity indices of bicyclic graphs with n ≥ 5 vertices. The extremal graphs are characterized. MSC 2000: 05C90; 05C35; 05C07

We generalize the concept of exclusive sum labelings of graphs (cf. [?]) and determine the exclusive sum number for several classes of hypergraphs. The results disclose a significant difference between graphs (i.e. 2-uniform hypergraphs) and ”genuine” hypergraphs.