A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

An understanding of the transfer (or generalization) of motor adaptations between legs and across tasks during walking has remained elusive due to limited research and mixed results. Here, we asked whether stepping sequences or task constraints introduced during walking prism-adaptation tasks influence generalization patterns. Forty subjects adapted to prism glasses in precision-walking or obst...

Matroids are important combinatorial structures and connect close-lywith graphs. Matroids and graphs were all generalized to fuzzysetting respectively. This paper tries to study  connections betweenfuzzy matroids and fuzzy graphs. For a given fuzzy graph, we firstinduce a sequence of matroids  from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matro...

‎the narumi-katayama index was the first topological index defined‎ ‎by the product of some graph theoretical quantities‎. ‎let $g$ be a ‎simple graph with vertex set $v = {v_1,ldots‎, ‎v_n }$ and $d(v)$ be‎ ‎the degree of vertex $v$ in the graph $g$‎. ‎the narumi-katayama ‎index is defined as $nk(g) = prod_{vin v}d(v)$‎. ‎in this paper,‎ ‎the narumi-katayama index is generalized using a $n$-ve...

Let G be a simple connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is k. Some formulas are obtained for computing the generalized polarity Wiener index of the Cartesian product and the tensor product of graphs in this article.

Williams, Jesse T. M.S., Department of Mathematics and Statistics, Wright State University, 2014. A New Proof for a Result of Kingan and Lemos. The prism graph is the planar dual of K5\e. Kingan and Lemos [4] proved a decomposition theorem for the class of binary matroids with no prism minor. In this paper, we present a different proof using fundamental graphs and blocking sequences.

matroids are important combinatorial structures and connect close-lywith graphs. matroids and graphs were all generalized to fuzzysetting respectively. this paper tries to study  connections betweenfuzzy matroids and fuzzy graphs. for a given fuzzy graph, we firstinduce a sequence of matroids  from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. a fuzzy matroid, named graph fuzzy matro...

In this paper, we revisit the concept of (normalized) closeness centrality a vertex in graph and investigate it some graphs under operations. Specifically, derive formulas that compute vertices shadow graph, complementary prism, edge corona, disjunction graphs.

A data-graph computation — popularized by such programming systems as Pregel, GraphLab, Galois, Ligra, PowerGraph, and GraphChi — is an algorithm that iteratively performs local updates on the vertices of a graph. During each round of a data-graph computation, a user-supplied update function atomically modifies the data associated with a vertex as a function of the vertex’s prior data and that ...