Problem solving is an analog to scientific method, wherein abduction and deduction operate in a cyclic fashion to generate and refine a series of hypotheses that purport to explain the observed data. Model Generative Reasoning implements this cycle through a family of operations on representations based on conceptual graphs. Specialize, the operator that implements abduction generates alternati...

We present a graph-based data model called GDM where database instances and database schemas are described by certain types of labeled graphs called instance graphs and schema graphs. For this data model we introduce two graph-manipulation operations, an addition and a deletion, that are based on pattern matching and can be represented in a graphical way. For these operations it is investigated...

In this paper, we show that the disjoint union of two cordial graphs one of them is of even size is cordial and the join of two cordial graphs both are of even size or one of them is of even size and one of them is of even order is cordial. We also show that Cm∪ Cn is cordial if and only if m+n ≡/ 2 (mod 4) and mCn is cordial if and only if mn ≡/ 2 (mod 4) and for m, n ≥ 3, Cm + Cn is cordial i...

In previous papers, Catlin introduced four functions, denoted S, S, S , and S , between sets of nite graphs. These functions proved to be very useful in establishing properties of several classes of graphs, including supereulerian graphs and graphs with nowhere zero kows for a xed integer k¿ 3. Unfortunately, a subtle error caused several theorems previously published in Catlin (Discrete Math. ...

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.

Let $G$ be a finite and simple graph with edge set $E(G)$‎. ‎The revised Szeged index is defined as‎ ‎$Sz^{*}(G)=sum_{e=uvin E(G)}(n_u(e|G)+frac{n_{G}(e)}{2})(n_v(e|G)+frac{n_{G}(e)}{2}),$‎ ‎where $n_u(e|G)$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$ and‎ ‎$n_{G}(e)$ is the number of‎ ‎equidistant vertices of $e$ in $G$‎. ‎In this paper...

Let $S= \{e_1,\,e_2‎, ‎\ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$‎. ‎The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the‎ ‎vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$‎, ‎where $d_i=1$ if $e_i\in M$ and $d_i=0$‎ ‎otherwise‎, ‎for each $i\in\{1,\ldots‎ , ‎k\}$‎. ‎We say $S$ is a global forcing set for maximal matchings of $G$‎ ‎if $...

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 graph of size n is said to be graceful when is possible toassign distinct integers from {0, 1, . . . , n} to its verticesand {|f(u)−f(v)| : uv ∈ e(g)} consists of n integers. inthis paper we present broader families of graceful graphs; these families are obtained via three different operations: the third power of a caterpillar, the symmetric product of g and k2 , and the disjoint :union: of g...