Abstract. Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. A graph is a ...

The idea of integral sum graphs was introduced by Harary (1994). A graph G is said to be an integral sum graph if its nodes can be given a labeling f with distinct integers, so that for any two distinct nodes u and v of G, uv is an edge of G if and only if f(u) + f(v) = f(w) for some node w in G. A tree is said to be a generalized star if it can be obtained from a star by extending each edge to...

Harary’s generalized Tic-Tac-Toe is an achievement game for polyominoes, where two players alternately put a stone on a grid board, and the player who first achieves a given polyomino wins the game. It is known whether the first player has a winning strategy in the generalized Tic-Tac-Toe for almost all polyominoes except the one called Snaky. GTTT(p, q) is an extension of the generalized Tic-T...

Often data in the real world have the property that the first digit 1 appears about 30% of the time, the first digit 2 appears about 17% of the time, and so on with the first digit 9 appearing about 5% of the time. This phenomenon is known as Benford’s law. This paper provides a simple explanation, suitable for nonmathematicians, of why Benford’s law holds for data that has been growing (or shr...

Classifying integral graphs is a hard problem that initiated by Harary and Schwenk in 1974. In this paper, with the help of character table, we treat corresponding for Cayley over semi-dihedral group SD8n = ?a,b | a4n b2 1; bab a2n-1?, n ? 2. We present several necessary sufficient conditions integrality SD8n, also obtain some simple terms Boolean algebra hai. particular, give groups SD2n (n?4)...