Let G be a (p,q) graph and A be a group. We denote the order of an element $a in A $ by $o(a).$  Let $ f:V(G)rightarrow A$ be a function. For each edge $uv$ assign the label 1 if $(o(f(u)),o(f(v)))=1 $or $0$ otherwise. $f$ is called a group A Cordial labeling if $|v_f(a)-v_f(b)| leq 1$ and $|e_f(0)- e_f(1)|leq 1$, where $v_f(x)$ and $e_f(n)$ respectively denote the number of vertices labelled w...

in this paper, a new molecular-structure descriptor, the general sum–connectivity co–index  is considered, which generalizes the first zagreb co–index and the general sum–connectivity index of graph theory. we mainly explore the lower and upper bounds in termsof the order and size for this new invariant. additionally, the nordhaus–gaddum–type resultis also represented.

The work analyses typical uses of attribute-like relations in conceptual graphs and identifies general sources of failure to convey intended meaning. These include relations that do not contain a semantic bond between their arguments, semantically superfluous concept types, and confusion between first-order and second-order levels. The analysis focuses on the semantics of physical quantities an...

Let Γ = (X, R) denote a distance-regular graph with diameter D ≥ 3 and distance function δ. A (vertex) subgraph ∆ ⊆ X is said to be weak-geodetically closed whenever for all x, y ∈ ∆ and all z ∈ X, δ(x, z) + δ(z, y) ≤ δ(x, y) + 1 −→ z ∈ ∆. Γ is said to be D-bounded whenever for all x, y ∈ X, x, y are contained in a common regular weak-geodetically closed subgraph of diameter δ(x, y). Assume Γ i...

Nurse Rostering Problem (NRP) or the Nurse Scheduling Problem (NSP) is a complex scheduling problem that affects hospital personnel on a daily basis all over the world and is known to be NP-hard.The problem is to decide which members of a team of nurses should be on duty at any time, during a rostering period of, typically, one month.It is very important to efficiently utilize time and effort, ...

Given any infinite structureM with a decidable first-order theory, we give a sufficient condition in terms of the Gaifman graph of M, which ensures that M can be expanded with some non-definable predicate in such a way that the first-order theory of the expansion is still decidable. LACL Technical Report 2007-06

‎A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$‎. ‎The total domination number of a graph $G$‎, ‎denoted by $gamma_t(G)$‎, ‎is~the minimum cardinality of a total dominating set of $G$‎. ‎Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004)‎, ‎6...