This thesis is focused on improving execution time and precision of scalable pointer analysis. Such an analysis statically determines the targets of all pointer variables in a program. We formulate the analysis as a directed graph problem, where the solution can be obtained by a computation similar, in many ways, to transitive closure. As with transitive closure, identifying strongly connected ...

A subgroup of the automorphism group a graph Γ is said to be half-arc-transitive on if its action transitive vertex set and edge but not arc Γ. Tetravalent graphs girths 3 4 admitting automorphisms have previously been characterized. In this paper we study examples girth 5. We show that, with two exceptions, all such only directed 5-cycles respect corresponding induced orientation edges. Moreov...

Let G = (V,E) be a multigraph (it has multiple edges, but no loops). We call G maximally edge-connected if λ(G) = δ(G), and G super edge-connected if every minimum edge-cut is a set of edges incident with some vertex. The restricted edgeconnectivity λ′(G) of G is the minimum number of edges whose removal disconnects G into non-trivial components. If λ′(G) achieves the upper bound of restricted ...

Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex 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} according as p is even or o...

We obtain several new dynamic algorithms for maintaining the transitive closure of a directed graph and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. Among our algorithms are: (i) A decremental algorithm for maintaining the transitive closure of a directed graph, through an arbitrary sequence of edge deletions, in O(mn) t...

We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (choose the transition probabilities on the edges to minimize the second-largest eigenvalue modulus of the transition probability matrix). Exploiting symmetry can lead to significant reduction in both number of optimization variables and size of matrices in solving the corresponding ...

Abstract A graph $\Gamma $ is called $(G, s)$ -arc-transitive if $G \le \text{Aut} (\Gamma )$ transitive on the set of vertices and s -arcs , where for an integer $s \ge 1$ -arc a sequence $s+1$ $(v_0,v_1,\ldots ,v_s)$ such that $v_{i-1}$ $v_i$ are adjacent $1 i s$ $v_{i-1}\ne v_{i+1}$ s-1$ . 2-transitive it $(\text{Aut} ), 2)$ but not 3)$ -arc-transitive. Cayley group G normal in $\text{Aut} n...

In the past, diierent authors developed distinct approaches to the problem of transitive orientation. This also resulted in diierent ideas and diierent theorems which seem unrelated. In this paper we show the connections between these theories and present a new algorithm to recognize a comparability graph. A comparability graph is an undirected graph G = (V; E), jV j = n, jEj = m, in which ever...

the $k$-th semi total point graph $r^k(g)$ of a graph $g$, is a graph obtained from $g$ by adding $k$ vertices corresponding to each edge and connecting them to endpoint of edge considered. in this paper, we obtain formulae for the resistance distance and kirchhoff index of $r^k(g)$.

Weakly s-arc transitive graphs are introduced and determined. A graph is said to be weakly s-arc transitive if its endomorphism monoid acts transitively on the set of s-arcs. The main results are: (1) A nonbipartite graph is weakly s-arc transitive if and only if it is s-arc transitive. (2) A tree with diameter d is weakly s-arc transitive for all 0 s d. (3) A bipartite graph with girth g = 2s ...