This paper deals with two types of graph labelings namely, the super (a, d)-edge antimagic total labeling and super (a, d)-vertex antimagic total labeling on the Harary graph C n. We also construct the super edge-antimagic and super vertex-antimagic total labelings for a disjoint union of k identical copies of the Harary graph.

The Kauffman-Harary conjecture is a conjecture for Fox’s colorings of alternating knots with prime determinants. We consider a conjecture for Alexander quandle colorings by referring to the Kauffman-Harary conjecture. We prove that this new conjecture is true for twist knots.

If G is a connected graph, then HA(G) = ∑ u6=v(deg(u) + deg(v))/d(u, v) is the additively Harary index and HM (G) = ∑ u6=v deg(u) deg(v)/d(u, v) the multiplicatively Harary index of G. G is an apex tree if it contains a vertex x such that G − x is a tree and is a k-apex tree if k is the smallest integer for which there exists a k-set X ⊆ V (G) such that G − X is a tree. Upper and lower bounds o...

Abstract In this paper, the exact formulae for the Harary indices of join, disjunction, symmetric difference, strong product of graphs are obtained. Also, the Schultz and modified Schultz indices of join and strong product of graphs are computed. We apply some of our results to compute the Harary, Schultz and modified Schultz indices of fan graph, wheel graph, open fence and closed fence graphs.

A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of ...

The domination number of graph is the smallest cardinality set G. A subset a vertex S G called if every element dominates G, meaning that not an connected and one distance from S. has become interesting research studies on several graphs k -connected such as circulant graphs, grids, wheels. This study aims to determine other k-connected Harary graph. method used pattern detection axiomatic dedu...

In this paper, we consider Harary graphs as candidate solutions for the design of a physical network topology that achieves a high level of reliability using unreliable network elements. Our network model, which is motivated by the use of all-optical networks for high-reliability applications, is one in which nodes are invulnerable and links are subject to failure in a statistically independent...

Professor Frank Harary has had a singular influence on graph theory through his own extensive original research, through the training of several researchers who themselves have made many important contributions, and through popularizing work, most significantly his text Graph Theory [1]. Frank Harary has contributed to a number of more advanced specialized texts, like that of Buckley and Harary...

We present new functional equations for the species of plane and of planar in the sense of Harary and Palmer, 1973 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e.a classiication of their structures according to their stabilizers. Therein result explicit formulas in terms of Catalan numbers for their associated generating series...

Assuming that G is a finite group and H subgroup of G, the graph known as relative coprime with respect to (denoted Γ_(G,H)) has vertices corresponding elements G. Two distinct x y are adjacent by an edge if only (|x|,|y|)=1 or belongs H. This paper will focus on finding general formula for some topological indices dihedral group. The study in theory offers valuable insights into structural pro...