In a graph G=(V,E), where every vertex is assigned 0, 1 or 2, f an assignment such that 0 has at least one neighbor 2 and all vertices labeled by are independent, then called outer independent Roman dominating function (OIRDF). The domination strengthened if 1, 3, each two neighbors double (OIDRDF). weight of (OIDRDF) OIRDF the sum f(v) for v?V. (double) number (?oidR(G)) ?oiR(G) minimum taken ...

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

We generalize some results of Ford and Roman constraining the possible behaviors of the renormalized expected stressenergy tensor of a free massless scalar field in two dimensional Minkowski spacetime. Ford and Roman showed that the energy density measured by an inertial observer, when averaged with respect to the observers proper time by integrating against some weighting function, is bounded ...

We consider two infinite games, played on a countable graph G given with an integer vertex labelling. One player seeks to construct a ray (a one-way infinite path) in G, so that the ray’s labels dominate or elude domination by an integer sequence being constructed by another player. For each game, we give a structural characterization of the graphs on which one player or the other can win, prov...

The Transliterated Search track has been organized for the second year in FIRE. The track has two subtasks. Subtask 1 on language labeling of words in code-mixed text fragments was conducted for 6 Indian languages: Bangla, Gujarati, Hindi, Malayalam, Tamil, Telugu, mixed with English. In Subtask 2 on retrieval of Hindi film lyrics, along with transliterated queries in Roman script, this year we...

Let G = (V,E) be a graph. A subset S of V is called a dominating set if each vertex of V −S has at least one neighbor in S. The domination number γ(G) equals the minimum cardinality of a dominating set in G. A minus dominating function on G is a function f : V → {−1, 0, 1} such that f(N [v]) = ∑ u∈N [v] f(u) ≥ 1 for each v ∈ V , where N [v] is the closed neighborhood of v. The minus domination ...

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...

Graphs of order n with fault-tolerant metric dimension have recently been characterized.This paper points out an error in the proof this characterization. We show that complete multipartite graphs also n, which provides infinite family counterexamples to Furthermore, we find exact values metric, edge mixed-metric dimensions, domination number, locating-dominating and metric-locating-dominating ...

etant donné le rapport réciproque entre la société et la littérature, et vu la dominance extraordinaire du roman, à l'état actuel, sur les autres expressions littéraires, on ne peut s'empêcher de s'interroger sur la cause et l'origine de la primauté du genre romanesque. certes, le roman ne date pas du xixe siècle; il est l'un des héritages des siècles précédents. néanmoins, son déploiement est ...