Vladimir Samodivkin

activity

20122020

most citedNote on the bondage number of graphs on topological surfaces

4 citations · 7 across the 12 of their papers we have counts for

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13 papers · 1 filter

math.CO2020

Excellent graphs with respect to domination: subgraphs induced by minimum dominating sets

Vladimir Samodivkin

A graph $G = (V, E)$ is $γ$ -excellent if $V$ is a union of all $γ$ -sets of $G$ , where $γ$ stands for the domination number. Let $I$ be a set of all mutually nonisomorphic gr…

math.CO2020

Domination related parameters in the generalized lexicographic product of graphs

Vladimir Samodivkin

In this paper we begin an exploration of several domination-related parameters (among which are the total, restrained, total restrained, paired, outer connected and total outer con…

math.CO2018

Changing and unchanging 2-rainbow independent domination

Pu Wu, Zehui Shao, Vladimir Samodivkin +3

For a function $f : V (G) \to {0, 1, 2}$ we denote by $V_{i}$ the set of vertices to which the value $i$ is assigned by $f$ , i.e. $V_{i} = {x \in V (G) : f (x) = i}$ . If…

math.CO2018

Changing and unchanging of the domination number of a graph: Path addition numbers

Vladimir Samodivkin

Given a graph $G = (V, E)$ and two its distinct vertices $u$ and $v$ . The $(u, v)$ - $P_{k}$ -{\em addition graph} of $G$ is the graph $G_{u, v, k - 2}$ obtained from disjoint union of $G$ an…

math.CO2017

Roman domination: changing, unchanging, $γ_{R}$ -graphs

Vladimir Samodivkin

A Roman dominating function (RD-function) on a graph $G = (V (G), E (G))$ is a labeling $f : V (G) \to {0, 1, 2}$ such that every vertex with label $0$ has a neighbor with l…

math.CO2016

Roman domination excellent graphs: trees

Vladimir Samodivkin

A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V \to {0, 1, 2}$ such that every vertex with label $0$ has a neighbor with label $2$ . The wei…

math.CO2016

Hypo-efficient domination and hypo-unique domination

Vladimir Samodivkin

For a graph $G$ let $γ (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient domination graph (or a hypo- $E D$ graph) if $G$ has no efficient domina…

math.CO2015

Roman domination in graphs: the class $R_{UVR}$

Vladimir Samodivkin

For a graph $G = (V, E)$ , a Roman dominating function $f : V \to {0, 1, 2}$ has the property that every vertex $v \in V$ with $f (v) = 0$ has a neighbor $u$ with $f (u) =…

math.CO2015

Changing of the domination number of a graph: edge multisubdivision and edge removal

Vladimir Samodivkin

For a graphical property $P$ and a graph $G$ , a subset $S$ of vertices of $G$ is a $P$ -set if the subgraph induced by $S$ has the property $P$ . The do…

math.CO2014★ 3 cited

On the Roman Bondage Number of Graphs on surfaces

Vladimir Samodivkin

A Roman dominating function on a graph $G$ is a labeling $f : V (G) \to {0, 1, 2}$ such that every vertex with label $0$ has a neighbor with label $2$ . The Roman dominatio…

math.CO2013

Upper bounds for domination related parameters in graphs on surfaces

Vladimir Samodivkin

In this paper we give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph in terms of order and…

math.CO2013

The bondage number of graphs on topological surfaces: degree-S vertices and the average degree

Vladimir Samodivkin

The bondage number $b (G)$ of a graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with larger domination number. An orientable surface $\mathbb{S}_…

math.CO2012★ 4 cited

Note on the bondage number of graphs on topological surfaces

Vladimir Samodivkin

The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. In this paper we present new upper bound…

Excellent graphs with respect to domination: subgraphs induced by minimum dominating sets

Domination related parameters in the generalized lexicographic product of graphs

Changing and unchanging 2-rainbow independent domination

Changing and unchanging of the domination number of a graph: Path addition numbers

Roman domination: changing, unchanging, γR​-graphs

Roman domination excellent graphs: trees

Hypo-efficient domination and hypo-unique domination

Roman domination in graphs: the class RUVR​

Changing of the domination number of a graph: edge multisubdivision and edge removal

On the Roman Bondage Number of Graphs on surfaces

Upper bounds for domination related parameters in graphs on surfaces

The bondage number of graphs on topological surfaces: degree-S vertices and the average degree

Note on the bondage number of graphs on topological surfaces

Roman domination: changing, unchanging, $γ_{R}$ -graphs

Roman domination in graphs: the class $R_{UVR}$