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## Injective and Relative Injective Zagreb Indıces of Graphs

#### Akram Alqesmah [1] , Anwar Alwardi [2] , R. Rangarajan [3]

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Let $G=(V,E)$ be a graph. The injective neighborhood of a vertex $u\in V(G)$ denoted by $N_{in}(u)$ is defined as $N_{in}(u)=\{v\in V(G):|\Gamma(u,v)|\geq 1\}$, where $|\Gamma(u,v)|$ is the number of common neighborhoods between the vertices $u$ and $v$ in $G$. The cardinality of $N_{in}(u)$ is called the injective degree of the vertex $u$ in $G$ and denoted by $deg_{in}(u)$, \cite{20}. In this paper, we introduce the injective Zagreb indices of a graph $G$ as $M_1^{inj}(G)=\sum_{u\in V(G)}\big[deg_{in}(u)\big]^2$, $M_2^{inj}(G)=\sum_{uv\in E(G)}deg_{in}(u)deg_{in}(v)$, respectively, and the relative injective Zagreb indices as $RM_1^{inj}(G)=\sum_{u\in V(G)}deg_{in}(u)deg(u)$, $RM_2^{inj}(G)=\sum_{uv\in E(G)}\big[deg_{in}(u)deg(v)+deg(u)deg_{in}(v)\big]$, respectively. Some properties of these topological indices are obtained. Exact values for some families of graphs and some graph operations are computed.
First injective Zagreb index, Second injective Zagreb index, First relative injective Zagreb index, Second relative injective Zagreb index
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 Bibtex @araştırma makalesi { konuralpjournalmath418208, journal = {Konuralp Journal of Mathematics}, issn = {}, eissn = {2147-625X}, address = {Mehmet Zeki SARIKAYA}, year = {}, volume = {6}, pages = {117 - 127}, doi = {}, title = {Injective and Relative Injective Zagreb Indıces of Graphs}, key = {cite}, author = {Rangarajan, R. and Alwardi, Anwar and Alqesmah, Akram} } APA Alqesmah, A , Alwardi, A , Rangarajan, R . (). Injective and Relative Injective Zagreb Indıces of Graphs. Konuralp Journal of Mathematics, 6 (1), 117-127. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/31478/418208 MLA Alqesmah, A , Alwardi, A , Rangarajan, R . "Injective and Relative Injective Zagreb Indıces of Graphs". Konuralp Journal of Mathematics 6 (): 117-127 Chicago Alqesmah, A , Alwardi, A , Rangarajan, R . "Injective and Relative Injective Zagreb Indıces of Graphs". Konuralp Journal of Mathematics 6 (): 117-127 RIS TY - JOUR T1 - Injective and Relative Injective Zagreb Indıces of Graphs AU - Akram Alqesmah , Anwar Alwardi , R. Rangarajan Y1 - 2018 PY - 2018 N1 - DO - T2 - Konuralp Journal of Mathematics JF - Journal JO - JOR SP - 117 EP - 127 VL - 6 IS - 1 SN - -2147-625X M3 - UR - Y2 - 2018 ER - EndNote %0 Konuralp Journal of Mathematics Injective and Relative Injective Zagreb Indıces of Graphs %A Akram Alqesmah , Anwar Alwardi , R. Rangarajan %T Injective and Relative Injective Zagreb Indıces of Graphs %D 2018 %J Konuralp Journal of Mathematics %P -2147-625X %V 6 %N 1 %R %U ISNAD Alqesmah, Akram , Alwardi, Anwar , Rangarajan, R. . "Injective and Relative Injective Zagreb Indıces of Graphs". Konuralp Journal of Mathematics 6 / 1 117-127.