Implication graphs are used to solve the test generation, redundancy identification, synthesis, and verification problems of digital circuits. We propose a new “oring” node structure to represent partial implications in a graph. The oring node is the contrapositive of the previously used “anding” node. An n-input gate requires one oring and one anding nodes to represent all partial implications...

The edge detour index polynomials were recently introduced for computing the edge detour indices. In this paper we find relations among edge detour polynomials for the 2-dimensional graph of $TUC_4C_8(S)$ in a Euclidean plane and $TUC4C8(S)$ nanotorus.

Let φ be Euler’s phi function. We prove that a vertex-transitive graph 0 of order n, with gcd(n, φ(n)) = 1, is isomorphic to a circulant graph of order n if and only if Aut(0) contains a transitive solvable subgroup. As a corollary, we prove that every vertex-transitive graph 0 of order n is isomorphic to a circulant graph of order n if and only if for every such 0, Aut(0) contains a transitive...

Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ρ and σ , where ρ is (m,n)semiregular for some integers m ≥ 1, n ≥ 2, and where σ normalizes ρ, cyclically permuting the orbits of ρ in such a way that σ has at least one fixed vertex. A halfarc-transitive graph is a vertexand edgebut not arc-transitive graph. In this arti...

Numerous networks as, for example, road networks, electrical networks and communication networks can be modeled by a graph. Many attempts have been made to determine how well such a network is "connected" or stated differently how much effort is required to break down communication in the system between at least some nodes. Two well-known measures that indicate how "reliable" a graph is are the...

An injective map f : E(G) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f*: V (G) → Z − {0} defined by f*(v) = (Sigma e∈Ev) f (e) is one-one, where Ev denotes the set of edges in G that are incident with a vetex v and f*(V (G)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} U {k(p+1)/2} accordin...

the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.

Sorting of transitive total ordered sets is one of the best investigated topics in Computer Science. A generalization of this is sorting an intransitive total ordered set which is more complex. While a transitive total ordered set (e. g. a subset of the real numbers) holds a ≥ b∧b ≥ a⇒ a ≥ c, this does not have to be true for a intransitive total ordered set. Only a → b ∨̇ b → a is claimed. Neve...

A transitive orientation of an undirected graph is an assignment of directions to its edges so that these directed edges represent a transitive relation between the vertices of the graph. Not every graph has a transitive orientation, but every graph can be turned into a graph that has a transitive orientation, by adding edges. We study the problem of adding an inclusion minimal set of edges to ...

Given a connected graph, in many cases it is possible to construct a structure tree that provides information about the ends of the graph or its connectivity. For example Stallings’ theorem on the structure of groups with more than one end can be proved by analyzing the action of the group on a structure tree and Tutte used a structure tree to investigate finite 2-connected graphs, that are not...