Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G ...

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...

Extraction of text embedded in scene images has many applications, such as license plate recognition, content based retrieval, text based indexing etc. As the appearances of the text in images are unpredictable, separating text pixels from the background is a challenging one. A new frame work is introduced here which uses edge enhanced MSER along with connected components for text extraction. C...

Let G be a simple connected graph of order n. Dcνe (G, i) the family vertex-edge dominating sets with cardinality i. The polynomial x) = is called domination where dcνe number vertex edge G. In this paper, we study some properties polynomials Gem Gn. Also obtain (Gn, and their coefficients. Also, find recursive formula, to derive

A digraph G = (V, E) with diameter D is said to be s-geodetic, for 1 ≤ s ≤ D, if between any pair of (not necessarily different) vertices x, y ∈ V there is at most one x → y path of length ≤ s. Thus, any loopless digraph is at least 1-geodetic. A similar definition applies for a graph G, but in this case the concept is closely related to its girth g, for then G is s-geodetic with s = b(g − 1)/2...

Let G = (V, A) be a digraph with diameter D 6= 1. For a given integer 2 ≤ t ≤ D, the t-distance connectivity κ(t) of G is the minimum cardinality of an x → y separating set over all the pairs of vertices x, y which are at distance d(x, y) ≥ t. The t-distance edge connectivity λ(t) of G is defined similarly. The t-degree of G, δ(t), is the minimum among the out-degrees and in-degrees of all vert...

An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processor and communication links, respectively. Connectivity is an important measurement for the fault tolerant in interconnection network. Two vertices is maximally local-connected if the maximum number of internally vertex-disjoint paths between them equals the minimum degree of these two vert...

Let G be a connected graph with maximum degree ∆(G). The irregularity index t(G) of G is defined as the number of distinct terms in the degree sequence of G. We say that G is maximally irregular if t(G) = ∆(G). The purpose of this note, apart from pointing out that every highly irregular graph is maximally irregular, is to establish upper bounds on the size of maximally irregular graphs and max...