A vertex w ? V resolves two elements x, y E if d(w,x) d(w,y). The mixed resolving set is a of vertices S, S any are resolved by some element S. minimum cardinality called the metric dimension graph G. This paper introduces three new general lower bounds for graph. exact values torus determined using one these bounds. Finally, illustrative examples and those known in literature presented on well...

An (m,n)-colored-mixed graph G=(V,A1,A2,⋯,Am,E1,E2,⋯,En) is a having m colors of arcs and n edges. We do not allow two or edges to have the same endpoints. A homomorphism from an G another H morphism φ:V(G)→V(H) such that each edge (resp. arc) mapped color (and orientation). T said be Pg(m,n)-universal if every in Pg(m,n) (the planar graphs with girth at least g) admits T. show exist for 2m+n≥3...

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of pure and mixed states, Von-Neumann entropy, separability of multipartite quantum states and quantum operations in terms of the graphs associated with quantum s...

Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs...

let g be a (p, q) graph. let f : v (g) → {1, 2, . . . , k} be a map. for each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of g if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

In this thesis we describe subclasses of a class of graphs with three types of edges, called loopless mixed graphs (LMGs). The class of LMGs contains almost all known classes of graphs used in the literature of graphical Markov models. We focus in particular on the subclass of ribbonless graphs (RGs), which as special cases include undirected graphs, bidirected graphs, and directed acyclic grap...