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**1 - 5**of**5**### IJMC The Maximal Total Irregularity of Some Connected Graphs

"... ABSTRACT The total irregularity of a simple graph is defined as , where denotes the degree of a vertex ∈ ( ). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices. ..."

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ABSTRACT The total irregularity of a simple graph is defined as , where denotes the degree of a vertex ∈ ( ). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.

### Irregularity Measures of Graph

, 2015

"... Abstract: Let G = (V, E), V = {1, 2, . . . , n}, be a simple graph without isolated vertices, with vertex degree sequence is measure of irregularity of graph G with the property I(G) = 0 if and only if G is regular, and I(G) > 0 otherwise. In this paper we introduce some new irregularity measure ..."

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Abstract: Let G = (V, E), V = {1, 2, . . . , n}, be a simple graph without isolated vertices, with vertex degree sequence is measure of irregularity of graph G with the property I(G) = 0 if and only if G is regular, and I(G) > 0 otherwise. In this paper we introduce some new irregularity measures.

### A study on total irregularities of certain graphs and digraphs

, 2016

"... Abstract: The total irregularity of a simple undirected graph G is denoted by irr t (G) and is defined as irr t (G) = In this paper, we introduce the notion of edge-transformation in relation to total irregularity of simple graphs with at least one cut edge as well as an edge-joint between two grap ..."

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Abstract: The total irregularity of a simple undirected graph G is denoted by irr t (G) and is defined as irr t (G) = In this paper, we introduce the notion of edge-transformation in relation to total irregularity of simple graphs with at least one cut edge as well as an edge-joint between two graphs. We also introduce the notion of total irregularity with respect to in-degree and out-degree in directed graphs. We also introduce the concept of total irregularity in respect of in-degree and out-degree in simple directed graphs. These invariants are called total in-irregularity and total out-irregularity, respectively. In this paper, we initiate a study on these parameters of given simple undirected graphs and simple digraphs.

### The Total Irregularity of some Composite Graphs

, 2015

"... The total irregularity of a simple undirected graph G = (V,E) is defined as irrt(G) = 1 2 u,v∈V (G) |dG(u) − dG(v)|, where dG(u) is the degree of the vertex u. In this paper we investigate the change of the total irregularity of graphs under various subdivision operations. Also, we present exact exp ..."

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The total irregularity of a simple undirected graph G = (V,E) is defined as irrt(G) = 1 2 u,v∈V (G) |dG(u) − dG(v)|, where dG(u) is the degree of the vertex u. In this paper we investigate the change of the total irregularity of graphs under various subdivision operations. Also, we present exact expressions and upper bounds on the total irregularity of different composite graphs such as the double graph, the extended double cover of a graph, the generalized thorn graph, several variants of subdivision corona graphs, and the hierarchical product graphs.